Aptitude  Probability
Exercise : Probability  General Questions
 Probability  Formulas
 Probability  General Questions
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} `  


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


= 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 
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