Question types

PART - 2 CH - 14 Probability question types

48 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

48
Questions
7
Question groups
5
Question types
Sample Questions

PART - 2 CH - 14 Probability questions

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

$A$ and $B$ are good tennis players of same level. If they play four games against each other, the probability of A exactly winning three games is:
  • A
    $\frac{1}{7}$
  • B
    $\frac{1}{2}$
  • $\frac{1}{4}$
  • D
    $\frac{3}{4}$

Answer: C.

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For any two events A and B, which of the following is true?
  • A
    $P ( A \cap B ) \geq P ( A )$
  • B
    $P ( A \cap$$B )= P ( A )$
  • $P ( A \cap B ) \leq P ( A )$
  • D
    None of these.

Answer: C.

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There are three red and three blue balls in a bag. A ball is drawn from the bag. Without keeping the first ball back in the bag, a second ball is drawn from the bag. The probability of both balls being of different colours is :
  • A
    $\frac{3}{10}$
  • B
    $\frac{1}{4}$
  • $\frac{3}{5}$
  • D
    $\frac{1}{2}$

Answer: C.

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On choosing one card randomly from a pack of 52 cards, the probability of getting a card of space is :
  • $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • C
    $\frac{3}{4}$
  • D
    $\frac{1}{13}$

Answer: A.

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Numbers 1 to 10 are written on 10 tickets. A ticket is drawn randomly. Find the probability of the number written on it to be a multiple of 3.
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There are 10 white and 15 red balls in a bag and 16 white and 9 red balls in another bag. One - one ball is drawn from each of the two bags. Find the probability of both balls to be of same colour.
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The probability of winning of $A$ in a race is $\frac{1}{3}$ and the probability of winning of $B$ is $\frac{1}{4}$. Find the probability of not winning of either of them.
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$A$ and $B$ played 12 games of chess in which $A$ won 6 games, two were drawn. They both decided to play three more games. Find the probability when :
(1) A wins three games,
(2) Two games were drawn,
(3) A and B wins alternately.
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The probability of a person being alive in next $25$ years is $3 / 5$ and of his wife to be alive in same $25$ years is $2 / 3$. Calculate the probability of :
(1) both being alive,
(2) none being alive,
(3) at least one to be alive,
(4) only wife to be alive.
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$A$ and $B$ are throwing two dice one after the other. If before $B$ throwing a 7, $A$ throws 6 then $A$ wins. If $B$ throws a 7 before $A$ throws a 6 then $B$ wins. If $A$ starts throwing then prove that the probability of winning of $A$ is $\frac{30}{61}.$
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There are three independent witnesses of any event that has occurred. A speaks truth three times out of four times. B speaks truth four times out of five times and C speaks truth five times out of six times. What is the probability of all the witnesses speaking in favour of the event with majority?
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$\text {A}$ speaks truth in $75 \%$ of the situations and $\text {B}$ in $80 \%$ of the situations. Find out in how many percent situations do they oppose each other?
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Part (A)Part (B)
1. There are three red, four white and five blue balls in a bag. On taking out two balls from the bag, the probability of their being of different colours is(a) $\frac{3}{7}$
2. 6 girls and 6 boys are sitting in a row. The probability of all girls sitting together is(b) $\frac{47}{66}$
3. The probability of getting 1 on both dice when thrown together is(c) $\frac{1}{132}$
4. Probability of 53 Fridays or 53 Saturdays in a leap year is(d) $\frac{6}{216}$
5. Probability of obtaining same number on throwing 3 dice is(e) $\frac{1}{36}$
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Part (A)Part (B)
1. Probability of obtaining three heads on tossing three coins(a) $\frac{1}{6}$
2. Probability of obtaining at least two heads on tossing three coins(b) $\frac{5}{6}$
3. Probability of getting a number less than 6 on throwing one dice(c) $\frac{1}{8}$
4. Probability of getting a sum of 5 on throwing two dice(d) $\frac{1}{9}$
5. Probability of getting a sum of 7 on throwing two dice(e) $\frac{1}{2}$
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