Exercise: Probability

Questions for: Probability

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
Answer: D

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) = 7 .
n(S) 8

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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
Answer: C

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) = 4 = 1 .
n(S) 36 9

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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
Answer: A

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) = 7 = 1 .
n(S) 21 3

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A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A:
10
21
B:
11
21
C:
2
7
D:
5
7
Answer: A

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then, n(S) = Number of ways of drawing 2 balls out of 7
= 7C2 `
= (7 x 6)
(2 x 1)
= 21.

Let E = Event of drawing 2 balls, none of which is blue.

n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.
= 5C2
= (5 x 4)
(2 x 1)
= 10.

P(E) = n(E) = 10 .
n(S) 21

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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
Answer: D

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) = 9 .
n(S) 20

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