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