CBSE Class 9 - Mathematics - Probability - Problems and Solutions

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