- If two coins are tossed, find the probability of the following events. (1) Getting at…
- If two dice are rolled simultaneously, find the probability of the following events.…
- There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket…
- A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the…
- A card is drawn at random from a pack of well shuffled 52 playing cards. Find…

###### Practice Set 5.4

Question 1.If two coins are tossed, find the probability of the following events.

(1) Getting at least one head.

(2) Getting no head.

Answer:

Sample Space, S=(HH,HT,TH,TT)

(1)Probability of getting at least one head, p(A)=

p(A)=

(3) Probability of getting no head, p(B)=

p(B)=

Question 2.

If two dice are rolled simultaneously, find the probability of the following events.

(1) The sum of the digits on the upper faces is at least 10.

(2) The sum of the digits on the upper faces is 33.

(3) The digit on the first die is greater than the digit on second die.

Answer:

(1) Probability of getting the sum of the digits on the upper faces is at least 10, p(A)=

We know the Favourable Cases are (Where the Sum of digits on the upper faces is at least 10):- (4,6), (5,5), (5,6), (6,4), (6,5), (6,6)- 6 cases

Total Number of Outcomes:- 36

p(A)=

(2) Probability of getting the sum of the digits on the upper faces is 33, p(B)=

Favorable Outcomes(Getting the sum of Digits on the upper Faces is 33)= 0 as the maximum sum could be 12p(B)=0

(3) (3) Probability of getting the digit on the first die is greater than the digit on second die, p(C)=

Favorable Outcomes are as follow:- (2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3),(6,4), (6,5)= 15 cases

p(C)=

Question 3.

There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn -

(1) shows an even number.

(2) shows a number which is a multiple of 5.

Answer:

(1) Probability of event that the ticket drawn shows an even number, p(E) =

p(E)=

(2) Probability of event that the ticket drawn shows a number which is a multiple of 5,

p(X) =

p(X)=

Question 4.

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is

(1) an odd number ?

(2) a multiple of 5 ?

Answer:

(1) Probability that the number formed is an odd number,

p(X) =

p(X)=

(2) Probability that the number formed is an odd number,

p(X) =

p(X)=

Question 5.

A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is -

(1) an ace. (2) a spade.

Answer:

(1) Probability that the card drawn is an ace, p(A)=

p(A)=

(2) Probability that the card drawn is a spade, p(B)=

p(B)=