Probability
Problems and Solutions (NCERT Exemplar Answers)
Problem 1: Two dice are thrown simultaneously 500 times. Each time the sum of numbers appearing on their top is noted and recorded as given in the following table:
Sum | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Frequency | 14 | 30 | 42 | 55 | 72 | 75 | 70 | 53 | 46 | 28 | 15 |
If the dice are thrown once more, what is the probability of getting a sum
(i) 3
(ii) more than 10
(iii) less than 5 or equal to 5
(iv) between 8 and 12
Solution: Click here to see the solution.
Problem 2: Here is an extract from a mortality table:
Age(in years) | 60 | 61 | 62 | 63 | 64 | 65 |
Number of persons surviving out of sample of one million | 16090 | 11490 | 8012 | 5448 | 3607 | 2320 |
(i) Based on this information, what is the probability of a person 'aged 60' of dying within a year?
(ii)What is the probability that a person 'aged 61'will live for 4 years?
Solution: Click here to see the solution.
Problem 3: A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information so obtained is listed in the following table:
Montly income (in ₹) | Number of Televisions/Households |
|||
0 | 1 | 2 | Above 2 | |
Less than 10000 | 20 | 80 | 10 | 0 |
10000-14999 | 10 | 240 | 60 | 0 |
15000-19999 | 0 | 380 | 120 | 30 |
20000-24999 | 0 | 520 | 370 | 80 |
25000 and above | 0 | 1100 | 760 | 220 |
Find the probability:
(i) of a household earning ₹ 10000-₹ 14999 per month and having exactly onr television.
(ii) of a household earning ₹ 25000 and more per month and owning 2 televisions.
(iii) of a household having no television.
Answer:
MCQs
Q1. In a medical examination of students of a class, the following blood groups are recorded:
Blood Group | A | AB | B | O |
Number of students | 10 | 13 | 12 | 5 |
A student is selected at random from the class, the probability that he/she has blood group B is
(a) 1/4
(b) 13/40
(c) 3/10
(d) 1/8
Answer:(c) 3/10
Q2. In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is
(a) 0.25
(b) 0.50
(c) 0.75
(d) 0.80
Answer: (c) 0.75
Q3. A die is thrown 1000 times and the outcomes were recorded as follows:
Outcomes | 1 | 2 | 3 | 4 | 5 | 6 |
Frequency | 180 | 150 | 160 | 170 | 150 | 190 |
If the die is thrown once more, than the probability that it shows 5 is
(a) 9/50
(b) 3/20
(c) 4/25
(d) 7/25
Answer: (b) 3/20
4. Two coins are tossed 1000 times and the outcomes are recorded as below:
Number of heads | 2 | 1 | 0 |
Frequency | 200 | 550 | 250 |
Based on this information, the probability for atmost one head is
(a) 1/5
(b) 1/4
(c) 4/5
(d) 3/4
Answer: (c) 4/5
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