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Probability MATHS - Probability

Rajasthan Board (RBSE) - STD 11 Science - MATHS (Rajasthan - English Medium). 287 questions in this chapter.

Question types

Probability question types

287 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

287
Questions
8
Question groups
5
Question types
Sample Questions

Probability questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark

The equation of the circle passing through (3, 6) and whose centre is (2, -1) is:

  • A
    x2 + y2 - 4x + 3y = 45
  • B
    x2 + y2 - 4x + 2y - 45 = 0
  • C
    x2 + y2 + 4x - 2y = 45
  • D
    x2+ y2 - 4x + 2y + 45 = 0
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Q 2M.C.Q (1 Marks)1 Mark

If a coin is tossed till the first head appears, then what will be the sample space?

  • A
    {H}
  • B
    {TH}
  • C
    {T, TH, HHT, HHHT, ..........}
  • D
    {H, TH, TTH, TTTH, .......}
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Q 3M.C.Q (1 Marks)1 Mark

The lines 2x−3y=5 and 3x−4y=7 are the diameters of a circle of area 154 sq.units. The equation of the circle is:

  • A
    x2 + y2 + 2x - 2y = 62
  • B
    x2 + y2 - 2x + 2y = 47
  • C
    x2 + y2 + 2x - 2y = 47
  • D
    x2 + y2 - 2x + 2y = 62
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Q 4M.C.Q (1 Marks)1 Mark

Equation of the circle with centre on the y - axis and passing through the origin and the point (2, 3) is:

  • A
    x2 + y2 + 13y = 0
  • B
    x2 + 3y2 + 13x + 3 = 0
  • C
    x2 + 6y2 - 13y = 0
  • D
    x2 + y2 + 13 + 3 = 0
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Q 6True False[1 Marks ]1 Mark
State whether the statements are True or False.
The probability of an occurrence of event A is 0.7 and that of the occurrence of event B is .3 and the probability of occurrence of both is 0.4
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Q 8True False[1 Marks ]1 Mark
State whether the statements are True or False.
The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11
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Q 9True False[1 Marks ]1 Mark
State whether the statements are True or False.
The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.
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Q 10True False[1 Marks ]1 Mark
State whether the statements are True or False.
If A and B are two candidates seeking admission in an engineering College. The probability that A is selected is .5 and the probability that both A and B are selected is at most 0.3. Is it possible that the probability of B getting selected is 0.7?
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Q 11Fill In The Blanks[1 Marks ]1 Mark
Fill in the blanks.
The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is __________.
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Q 12Fill In The Blanks[1 Marks ]1 Mark
Fill in the blanks.
If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and $\text{P}(\text{A}\cap\text{B})=0.1,$ then the value of $\text{P}(\text{A}\cap\bar{\text{B}})$ is ____________.
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Q 161 Marks Question1 Mark
If 4-digit numbers greater than 5000 are randomly formed from the digits 0, 1, 3, 5, and 7. What is the probability of forming a number divisible by 5 when the repetition of digits is not allowed?
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Q 171 Marks Question1 Mark
If 4-digit numbers greater than 5000 are randomly formed from the digits 0, 1, 3, 5, and 7 what is the probability of forming a number divisible by 5 when the digits are repeated?
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Q 181 Marks Question1 Mark
In a certain lottery 10,000 tickets are sold and, ten equal prizes are awarded. What is the probability of not getting a prize if you buy 10 tickets?
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Q 191 Marks Question1 Mark
In a certain lottery 10,000 tickets are sold and, ten equal prizes are awarded. What is the probability of not getting a prize if you buy two tickets?
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Q 201 Marks Question1 Mark
In a certain lottery 10,000 tickets are sold and, ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket?
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Q 212 Marks Questions2 Marks
Three letters are written to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
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Q 232 Marks Questions2 Marks
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that at least one will be green?
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Q 242 Marks Questions2 Marks
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that all will be blue?
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Q 252 Marks Questions2 Marks
There are four men and, six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
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Q 263 Marks Question3 Marks
From the employees of a company, 5 persons are selected to represents them in the managing committee of the company particulars of five persons are as follows:

S.No. Name Sex Age in years
1 Harish M 30
2 Rohan M 33
3 Sheetal F 46
4 Alice F 28
5 Salim M 41

A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?

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Q 273 Marks Question3 Marks
Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that,
  1. you both enter the same section?
  2. you both enter the different sections?
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Q 283 Marks Question3 Marks
The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e. from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
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Q 293 Marks Question3 Marks
A fair coin is tossed four times, and a person win Re 1 for each head, and lose Rs. 1.50 for each tail that turns up. Form the sample space, calculate how many different amounts of money he can have after four tosses and the probability of having each of these amounts.
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Q 315 Marks Questions5 Marks
A and B are two events such that P(A) = 0.54, P(B) = 0.69 and $P(A \cap B) = 0.35$. Find
  1. $P(A \cup B)$
  2. $P(A'\cap B')$
  3. $P(A\cap B')$
  4. $P( B\cap A')$
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Q 335 Marks Questions5 Marks
In a lottery, a person chosen, six different natural numbers at random from 1 to 20 and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?
[Hint order of the numbers is not important.]
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Q 345 Marks Questions5 Marks
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
A: the sum is greater than 8, B: 2 occurs on either die.
C: the sum is at least 7 and a multiple of 3
which pairs of these events are mutually exclusive?
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Q 355 Marks Questions5 Marks
A die is thrown. Describe the following events:

  1. A: a number less than 7
  2. B: a number greater than 7
  3. C: a multiple of 3
  4. D: a number less than 4
  5. E: an even number greater than 4
  6. F: a number not less than 3

Also find ${A\cup B}$, ${A\cap B}$, ${B\cup C}$, ${E\cap F}$, ${D\cap E}$, A –C, D–E, ${E\cap F'}$, F'.

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Q 36Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The probability of drawing either an ace or a king from a pack of cards in a single draw is $\frac{2}{13}.$
Reason: For two events A and B which are not mutually exclusive,
 $\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B}).$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 37Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Consider the experiment of rolling a die. Then, sample space is S = {1, 2, 3, 4, 5, 6}.
Assertion: The event EF : “the number appears on the die is a multiple of 7”, is an impossible event.
Reason: The event F : “the number turns up is odd or even”, is a sure event.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 38Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A coin is tossed and then a die is rolled only in case a head is shown on the coin. The sample space for the experiment is S = (H1, H2, H3, H4, H5, H6, T}.
Reason: 2 boys and 2 girls are in room X, and 1 boy and 3 girls are in room Y. Then, the sample space for the experiment in which a room is selected and then a person, is S = {XB1, XB2, XG1, XG2, YB3, YG3, YG4, YG5} where Bi, denote the boys and Gj, denote the girls.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 39Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A coin is tossed. If it shows head, we draw a ball from a bag consisting of 3 brown and 4 red balls; if it shows tail we throw a die, then the sample space of this experiment is S = {HB1, HB2, HB3, HR1, HR2, HR3, HR4, T1, T2, T3, T4, T5, T6}.
Reason: Consider the experiment in which a coin is tossed repeatedly until a head comes up, then the sample space is S = {H, TH, TTH, TTTH,........ }.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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Q 40Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Consider the experiment of rolling a die. Then, sample space is S = {1, 2, 3, 4, 5, 6}.
Assertion: If sample space of an experiment is S = {1, 2, 3, 4, 5, 6} and the events A and B are defined as
A : “a number less than or equal to 3 appears”
B :“anumber greater than or equal to 3 appears”,
then A and B are exhaustive events.
Reason: Events are exhaustive if atleast one of them necessarily occur whenever the experiment is performed.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
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