CBSE Important Questions
Probability
- A coin is tossed 1000 times with the following frequencies:
Head: 455, Tail: 545 compute the probability for each event.
- Two coins are tossed simultaneously 500 times, and we get- Two heads: 105 times,
One head: 275 times, No head: 120 times, find the probability of occurrence of each of these events.
- A die is thrown 1000 times with the frequencies for the outcome 1, 2, 3, 4, 5 and 6 as given in the following table:
Outcome |
1 |
2 |
3 |
4 |
5 |
6 |
Frequency |
179 |
150 |
157 |
149 |
1175 |
190 |
Find the probability of getting each outcome.
- The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times.
(i) What is the probability that on a given day it was correct?
(ii) What is the probability that it was not correct on a given day?
- The percentage (%) of the marks obtained by a student in the monthly unit test are given below:
Unit test |
I |
II |
III |
IV |
V |
Percentage (%) of the marks obtained |
69 |
71 |
73 |
68 |
74 |
Based on this data, find the probability that the student gets more than 70% marks in a unit test.
- An insurance company selected 2000 drivers at random (i.e. without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table:
Age of drivers
(in years |
Accidents in one year |
0 |
1 |
2 |
3 |
Over 3 |
18-29 |
440 |
160 |
110 |
61 |
35 |
30-50 |
505 |
125 |
60 |
22 |
18 |
Above 50 |
360 |
45 |
35 |
15 |
9 |
Find the probabilities of the following events for a driver chosen at random from the city:
(i) Being 18-29 years of age and having exactly 3 accidents in one year.
(ii) Being 30-50 years of age and having one or more accidents in a year.
(iii) Having no accidents in one year.
- In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
- 1500 families with 2 children were selected randomly, and the following data were recorded:
Numbers of girls in a family |
2 |
1 |
0 |
Number of families |
475 |
814 |
211 |
Compute the probability of a family, chosen at random, having
(i) 2 girls
(ii) 1 girl
(iii) No girl.
- 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 |
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
- An organization selected 2400families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family, the information gathered is listed in the table below:
Monthly in come
(in Rs) |
Vehicles per family |
0 |
1 |
2 |
Above 2 |
Less than 7000 |
10 |
160 |
25 |
0 |
7000-10000 |
0 |
305 |
27 |
2 |
10000-13000 |
1 |
535 |
29 |
1 |
13000-16000 |
2 |
469 |
59 |
25 |
16000 or more |
1 |
579 |
82 |
88 |
Suppose a family is chosen. Find the probability that the family chosen is
(i) Earning Rs 10000-13000 per month and owing exactly 2 vehicles.
(ii) Earning Rs 16000 or more per month and owning exactly 1 vehicle.
(iii) Earning less than Rs 7000 per month and does not own any vehicle.
(iv) Earning Rs 13000-16000 per month and owning more than 2 vehicles.
(v) Owning not more than 1 vehicle.
- Eleven bags of wheat flour, each marked 5 kg, actually contained following weights of flour (in kg): 4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00 find the probability that any of these Bags chosen at random contains more than 5 kg of flour.
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