## 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

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?

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.

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

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

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

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