# Probability

## Probability

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 Question 1
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
 A 1/2 B 2/5 C 8/15 D 9/20
Question 1 Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) =(n(E)/n(S)) ==>9/20
 Question 2
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? .
 A 1/3 B 3/4 C 7/19 D 8/21
Question 2 Explanation:
Total number of balls = (8 + 7 + 6) = 21. Let E = event that the ball drawn is neither red nor green = event that the ball drawn is blue. n(E) = 7. P(E) = (n(E)/n(S)) ==>7/21 ==>1/3 .
 Question 3
What is the probability of getting a sum 9 from two throws of a dice?
 A 1/6 B 1/8 C 1/9 D 1/12
Question 3 Explanation:
In two throws of a dice, n(S) = (6 x 6) = 36. Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}. P(E) = (n(E)/n(S)) ==>4/36 ==>1/9 .
 Question 4
Three unbiased coins are tossed. What is the probability of getting at most two heads?
 A 3/4 B 1/4 C 3/8 D 7/8
Question 4 Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH} Let E = event of getting at most two heads. Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}. P(E) = (n(E)/n(S)) ==>7/8
 Question 5
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?
 A 1/2 B 3/4 C 3/8 D 5/16
Question 5 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)/n(S)) ==>27/36 ==>3/4
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