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15 Mar 2019, 07:14
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D
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Difficulty:
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Question Stats:
49% (01:01) correct
51%
(01:10)
wrong
based on 689
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If event \(A\) and event \(B\) are independent, is the probability that both event \(A\) and event \(B\) occur greater than 0.3?
(1) Probability that \(A\) will occur is 0.25
(2) Probability that \(B\) will NOT occur is 0.71
(1) Probability that \(A\) will occur is 0.25
(2) Probability that \(B\) will NOT occur is 0.71
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15 Mar 2019, 07:18
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Official Solution:
If event \(A\) and event \(B\) are independent, is the probability that both event \(A\) and event \(B\) occur greater than 0.3?
Notice that since events \(A\) and \(B\) are independent, then the probability that both occur, equals to the product of their individual probabilities, so \(P(A \text { and } B)=P(A)*P(B)\). Also notice that \(0 \le P(A) \le 1\) and \(0 \le P(B) \le1\).
(1) Probability that \(A\) will occur is 0.25.
Since \(P(A)=0.25\), then \(P(A \text { and } B)=P(A)*P(B) \le 0.25 \lt 0.3\). Sufficient.
Or consider the following: how can the probability that both Event \(A\) and Event \(B\) will happen be more than individual probability of each happening? So, the probability that both happen cannot be more than 0.25.
(2) Probability that B will NOT occur is 0.71.
The same here: since \(P(B)=1-0.71=0.29\), then \(P(A \text { and } B)=P(A)*P(B) \le 0.29 \lt 0.3\). Sufficient.
Answer: D
If event \(A\) and event \(B\) are independent, is the probability that both event \(A\) and event \(B\) occur greater than 0.3?
Notice that since events \(A\) and \(B\) are independent, then the probability that both occur, equals to the product of their individual probabilities, so \(P(A \text { and } B)=P(A)*P(B)\). Also notice that \(0 \le P(A) \le 1\) and \(0 \le P(B) \le1\).
(1) Probability that \(A\) will occur is 0.25.
Since \(P(A)=0.25\), then \(P(A \text { and } B)=P(A)*P(B) \le 0.25 \lt 0.3\). Sufficient.
Or consider the following: how can the probability that both Event \(A\) and Event \(B\) will happen be more than individual probability of each happening? So, the probability that both happen cannot be more than 0.25.
(2) Probability that B will NOT occur is 0.71.
The same here: since \(P(B)=1-0.71=0.29\), then \(P(A \text { and } B)=P(A)*P(B) \le 0.29 \lt 0.3\). Sufficient.
Answer: D
16 Mar 2019, 11:04
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D is correct
1) P(A) = .25
If P(B) = 1 (greatest value), then this would still be .25 and less than .3. So no matter what the probability of P(B), this would never be greater than .3.
SUFFICIENT
2) P(not B) = .71 or P(B) = .29. Same reasoning found in 1).
SUFFICIENT
1) P(A) = .25
If P(B) = 1 (greatest value), then this would still be .25 and less than .3. So no matter what the probability of P(B), this would never be greater than .3.
SUFFICIENT
2) P(not B) = .71 or P(B) = .29. Same reasoning found in 1).
SUFFICIENT
