Question 11
Find the probability of getting 53 Sundays in a i) leap year ii) non leap year.
Solution
i) A leap year has 366 days. i.e there will be 52 Sundays and 2 day will be left.
This 2 day could be (Sun M), (M T), (T We), (We Th), (Th Fr), (Fr Sa), (Sa
Su).
Of these total 7 outcomes, the favourable outcomes are 2.
Hence the probability of getting 53 Sundays = 2 / 7.
ii) A non-leap year has 365 days. i.e there will be 52 Sundays and 1 day will be
left.
This 1 day could be Sunday, Monday, Tuesday, Wednesday, Thursday, friday
, Saturday, Sunday.
Of these total 7 outcomes, the favourable outcomes are 1.
Hence the probability of getting 53 Sundays = 1 / 7.
Question 12
A bag contains 5 red and some blue balls. If the probability of drawing a blue ball is double
that of a red ball, determine the number of blue ball in the bag.
Solution
x = 10
Question 13
A bag contains a red ball, a blue ball and a yellow ball, all the balls being
of the same size. Kritika takes out a ball from the bag without looking into it. What is the
probability that she takes out the
(i) yellow ball?
(ii) red ball?
(iii) blue ball?
Solution
Kritika takes out a ball from the bag without looking into it. So, it isequally likely that
she takes out any one of them.
Let Y be the event ‘the ball taken out is yellow’, B be the event ‘the ball taken
out is blue’, and R be the event ‘the ball taken out is red’.
Now, the number of possible outcomes = 3.
(i) The number of outcomes favourable to the event Y = 1.
So , P(Y) = 1/3
(ii) P(R) = 1/3
(iii) P(B) = 1/3
Question 14
There are 1000 sealed envelope in a box. 100 of them contains cash prize of Rs.100 each,
200 of them contains cash prize of Rs.75 each, 300 of them contains cash prize of Rs.50
each, and rest do not have any cash prize. If they are shuffled and an envelope is picked up
out then find the probability of that it contain no cash prize.
Solution
No of envelope contain cash prize = 100 + 200 + 300 = 600. Therefore, no of envelope
contain no cash prize = 1000 – 600 = 400. Its prob. = 400/1000 = 2/5
Question 15
A bag contains 5 red cards, 3 black cards and 2 green cards. What is the probability of
getting
i) one white card
ii) one black card
iii) neither a red card nor a black card
Solution
i) 0
Ii) 3/10
iii) 2/10
Question 16
Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally
likely to visit the shop on any one day as on another. What is the probability that both will visit the
shop on consecutive days?
Solution
5/18
Question 17
A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random from the bag. Find the
probability that the drawn ball is neither white nor black.
Solution
1/4
Question 18
A group consists of 12 persons , of which 3 are extremely patient other 6 are extremely honest and
rest are kind . A person is selected at random. Assuming that each person is equally likely to be
selected, find the probability of selecting a person who is extremely kind or honest.
Solution
3/4
Question 19
There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of 100 rupees
each, 100 of them contain a cash prize of 50 rupees each and 200 of them contain a cash prize
of 10 rupees each and rest do not contain any cash prize . If they are well shuffled and an
envelope is picked up out, what is the probability that it contains no cash prize?
Solution
There are 1000 envelopes in a box.
Number of envelopes containing no cash prize= 1000-(10+100+200)=690
Required probability=690/1000 =0.69
Question 20
Prateek and Ritesh are playing a game with number tokens. Each of them has four number
tokens 2,3,4 and 5. A token is randomly picked by each of them from their stack
simultaneously. If the sum of the numbers picked by each one of them is a prime number,
Pratek wins the game and if it is a composite number, then Ritesh wins the game.
Find the probability of each of them winning the game and state who has a higher probability
of winning the game.
Solution
Total number of outcomes= 16
Number of favourable outcomes for Prateek to win the game=6
Probability that Prateek wins the game=6/16 = 3/8
Probability that Ritesh wins the game= 1-3/8 = 5/8
Hence, Ritesh has a higher probability of winning the game.
SELF ASSESSMENT
Q1. Sachin and Saurav are playing with dice . Sachin throws two dice once and compute the product of the
two numbers appearing on the top of the dice . Saurav throws one die and square the number appearing on the top of the die . Who has the better chance of getting the number 36 ? Why?
Q2. A game of chance consists of spinning an arrow which comes to rest pointing at one
of the numbers 1, 2,3,4,5,6,7,8 and these are equally likely outcomes.
What is the probability that it will point at
(i) a prime number?
(ii) a perfect square number?
(iii) a number greater than 2?
Q3. Two dice are numbered 1,2,3,4,5,6 and 1,2,2,3,3,4 respectively . They are
thrown simultaneously and the sum of the numbers appearing on the top of the
dice are noted . Write all the possible outcomes and find the probability of
getting
(i) sum 7 (ii) Sum is a perfect square number
Q4. A card is drawn at random from a pack of 52 cards, one card is drawn at random .Find the
probability that the card drawn is neither an ace not a king.
Q5.Find the probability that a number selected at random from the numbers 3,4,4,4,5,5,6,6,6,7
will be their mean.
