Probability Examples 3

In this class, We discuss Probability Examples 3.

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Example 1:

Three students are randomly chosen from a class of 12 boys and four girls.

Find the probability for three students chosen one after another to be boys?

Solution:

Event A: First time should be a boy

Event B: Second time should be a boy

Event C: Third time should be a boy.

Three events should happen. A ∩ B ∩ C

From multiplicative law P(A ∩ B ∩ C) = P(A) P(B|A) P(C|A∩B)

P(A) = 12c1/16c1

P(B|A) = 11c1/15c1

P(C|A∩B) = 10c1/14c1

P(A ∩ B ∩ C) = 12/16 * 11/15 * 10/14

Example 2:

Two aeroplanes bomb a target in succession.

The probability of each scoring a hit is 0.3 and 0.2, respectively.

The second will bomb only if the first misses the target.

Find the probability.

1) Target is hit.

2) Both fail to hit.

Solution:

1) Target is hit A U (A’ ∩ B)

Event A: The first aeroplane hit the target.

Event B: Second aeroplane hit the target.

A U (A’ ∩ B) the two events are mutually exclusive events.

P(A U (A’ ∩ B)) = P(A) + P(A’∩B) from addition theorem.

A’ ∩ B are independent events.

P(A’∩B) = P(A’) P(B)

P(A U (A’ ∩ B) = P(A) + P(A’)P(B)

P(A U (A’ ∩ B) = 0.3 + 0.7 0.2

P(A U (A’ ∩ B) = 0.44

2) Both fail. A’ ∩ B’

P(A’ ∩ B’) = P(A’) P(B’)

P(A’ ∩ B’) = 0.7 0.8

P(A’ ∩ B’) = 0.56