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For a certain probability experiment the probability that
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10 Mar 2020, 11:05
10 Mar 2020, 11:05
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For a certain probability experiment the probability that event A will occur is 3/4 and the probability that event B will occur is 1/2 . Which of the following values could be the probability that event A ∩ B will occur.
A)1/6
B)1/5
C)1/3
D)2/3
E)3/4
A)1/6
B)1/5
C)1/3
D)2/3
E)3/4
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Re: For a certain probability experiment the probability that
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11 Mar 2020, 11:18
11 Mar 2020, 11:18
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Hm3105 wrote:
For a certain probability experiment the probability that event A will occur is 3/4 and the probability that event B will occur is 1/2 . Which of the following values could be the probability that event A ∩ B will occur.
A)1/6
B)1/5
C)1/3
D)2/3
E)3/4
A)1/6
B)1/5
C)1/3
D)2/3
E)3/4
Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B
=> Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B
=> Probability of A U B = 3/4 + 1/2 - Probability of A ∩ B
=> Probability of A U B = 5/4 - Probability of A ∩ B
The maximum value of Probability of A U B is 1
=> Probability of A ∩ B = 5/4 - 1 = 1/4 or higher
=> Minimum value of Probability of A ∩ B = 1/4
However, the maximum value of Probability of A ∩ B will be the smaller of the individual probabilities of A and B = 1/2
The only value between (inclusive) 1/4 and 1/2 is 1/3
Answer C
General Discussion
Re: For a certain probability experiment the probability that
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11 Mar 2020, 12:04
11 Mar 2020, 12:04
sujoykrdatta wrote:
Hm3105 wrote:
For a certain probability experiment the probability that event A will occur is 3/4 and the probability that event B will occur is 1/2 . Which of the following values could be the probability that event A ∩ B will occur.
A)1/6
B)1/5
C)1/3
D)2/3
E)3/4
A)1/6
B)1/5
C)1/3
D)2/3
E)3/4
Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B
=> Probability of A U B = Probability of A + Probability of B - Probability of A ∩ B
=> Probability of A U B = 3/4 + 1/2 - Probability of A ∩ B
=> Probability of A U B = 5/4 - Probability of A ∩ B
The maximum value of Probability of A U B is 1
=> Probability of A ∩ B = 5/4 - 1 = 1/4 or higher
=> Minimum value of Probability of A ∩ B = 1/4
However, the maximum value of Probability of A ∩ B will be the smaller of the individual probabilities of A and B = 1/2
The only value between (inclusive) 1/4 and 1/2 is 1/3
Answer C
Shouldn't the max value of A∩B be the bigger of the two individual probability? Please explain this part
