OverviewExercise"No one is as deaf as the man who will not listen."
 (Proverb)

6. 
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

Answer: Option
Explanation:
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E 
= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} 
n(E) = 27.
P(E) = 
n(E) 
= 
27 
= 
3 
. 
n(S) 
36 
4 

7. 
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

Answer: Option
Explanation:
Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S) 
= Number ways of selecting 3 students out of 25 

= ^{25}C_{3} ` 

= 
(25 x 24 x 23) 
(3 x 2 x 1) 


= 2300. 
n(E) 
= (^{10}C_{1} x ^{15}C_{2}) 

= 

10 x 
(15 x 14) 

(2 x 1) 


= 1050. 
P(E) = 
n(E) 
= 
1050 
= 
21 
. 
n(S) 
2300 
46 

8. 
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

Answer: Option
Explanation:
P (getting a prize) = 
10 
= 
10 
= 
2 
. 
(10 + 25) 
35 
7 

9. 
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? 
Answer: Option
Explanation:
Let S be the sample space.
Then, n(S) = ^{52}C_{2} = 
(52 x 51) 
= 1326. 
(2 x 1) 
Let E = event of getting 2 kings out of 4.
n(E) = ^{4}C_{2} = 
(4 x 3) 
= 6. 
(2 x 1) 
P(E) = 
n(E) 
= 
6 
= 
1 
. 
n(S) 
1326 
221 

10. 
Two dice are tossed. The probability that the total score is a prime number is:

Answer: Option
Explanation:
Clearly, n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.
Then E 
= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) } 
n(E) = 15.
P(E) = 
n(E) 
= 
15 
= 
5 
. 
n(S) 
36 
12 


