Probability Maths - Probability

The probability of an impossible event is:

1. 1
2. 0
3. Less than 0
4. Greater than 1

The probability of an event of a trial is: 

1. 1
2. 0
3. Less than 1
4. More than 0

The probability of a certain event is:

1. 0
2. 1
3. Greater than 1
4. Less than 0

Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.

Concentration of SO2	0.00 - 0.04	0.04 - 0.08	0.08 - 0.12	0.12 - 0.16	0.16 - 0.20	0.20 - 0.24
No. of days	4	8	9	2	4	3

Find the probability of the concentration of sulphur dioxide in the interval 0.12 - 0.16 on any of these days.

following table show the birth month of 40 students in class IX:

Jan	Feb	Mar	Apr	May	June	July	Aug	Sep	Oct	Nov	Dec
3	4	2	2	5	1	2	6	3	4	4	4

Find the probability that a student is born in August.

Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:
Two heads: 95 times
One heads: 290 times
No heads: 115 times
Find the probability of occurrence of each of these events.

To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is recorded in the following table:

Opinion	Like	Dislike
Number of students	135	65

Find the probability that a student chosen at random:

1. Likes Mathematics
2. Does not like it.

The percentage of marks obtained by a student in the monthly unit tests are given below:

Unit Test	I	II	III	IV	V
Percentage of Mark Obtained	69	71	73	68	76

Find the probability that the student gets:

1. More than 70% marks.
2. Less than 70% marks.
3. A distinction

Eleven bags of wheat flour, each marked 5kg, actually contained the following weights of flour (in Kg).

4.97

5.05

5.08

5.03

5

5.06

5.08

4.98

5.04

5.07

5

Find the probability that any of these bags chosen at random contains more than 5kg of flour.

A coin is tossed 1000 times with the following frequencies:
Head: 455, Tail = 545.
Compute the probability of each event.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome	3 heads	2 heads	1 head	No head
Frequency	23	72	77	28

Find the probability of getting at most two heads.

The Blood group table of 30 students of class IX is recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O
A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
A student is selected at random from the class from blood donation. Find the probability that the blood group of the student chosen is:

1. A
2. B
3. AB
4. O

In Q.No. 7, what is the probability of getting at least two heads?

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that a ball played:

1. He hit boundary
2. He does not hit a boundary.

Given below is the frequency distribution of wages (in ₹) of 30 workers in certain factory:

Wages(in ₹)	110-130	130-150	150-170	170-190	190-210	210 -230	230-250
No of workers	3	4	5	6	5	4	3

A worker is selected at random. Find the probability that his wages are:

1. Less than ₹ 150
2. At least ₹ 210
3. More than or equal to 150 but less than ₹ 210

Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:

Outcome	No head	One head	Two head	Three head
Frequency	14	38	36	12

If the three coins are tossed simultaneously again, compute the probability of:

1. 2 heads coming up.
2. 3 heads coming up.
3. At least one Head coming up.
4. Getting more Tails than Heads.
5. Getting more heads than tails.

The following table gives the life time of 400 neon lamps:

Life time(in hours)	300 - 400	400 - 500	500 - 600	600 - 700	700 - 800	800 - 900	900 -1000
Number of lamps:	14	56	60	86	74	62	48

A bulb is selected at random. Find the probability that the lifetime of a selected bulb is:

1. Less than 400
2. between 300 to 800 hours
3. At least 700 hours

Define probability of an event.

1500 families with 2 children were selected randomly, and the following data were recorded:

No of girls in a family	0	1	2
No of girls	211	814	475

If a family is chosen at random, compute the probability that it has:

1. No girl.
2. 1 girl.
3. 2 girls.
4. At most one girl.
5. More girls than boys.