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28 Nov 2024, 07:45
Kudos
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Hi Guys my probability concepts are still weak so if someone can please help me:
1- P(A) = 0.25, what if the probability of P(B)= 0.2, then P (A and B) = 0.25 x 0.2 = 0.5 > 0.3. What if P(B) = 0.1
then P (A and B) = 0.25 x 0.1 = 0.025 < 0.3@
Thank you
Bunuel
1- P(A) = 0.25, what if the probability of P(B)= 0.2, then P (A and B) = 0.25 x 0.2 = 0.5 > 0.3. What if P(B) = 0.1
then P (A and B) = 0.25 x 0.1 = 0.025 < 0.3@
Thank you
Bunuel
28 Nov 2024, 07:54
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devarpanc
Bunuel
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
Hi Guys my probability concepts are still weak so if someone can please help me:
1- P(A) = 0.25, what if the probability of P(B)= 0.2, then P (A and B) = 0.25 x 0.2 = 0.5 > 0.3. What if P(B) = 0.1
then P (A and B) = 0.25 x 0.1 = 0.025 < 0.3@
Thank you
Bunuel
0.25 x 0.2 = 0.05, NOT 0.5.
Hope this helps.
