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P(AandB) = pA + pB - p(AintersectionB)
0.6= 0.4 + p(B) - 0.25
= 0.45
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you can state both equations only if they are independent from each other ...
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hirendhanak
P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + P(B) - 0.25
P(B) = 0.45


Hi.

Can u tell me wat is P(AandB)????

Please clear my doubt.

regards,
Rrsnathan.
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hirendhanak
P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + P(B) - 0.25
P(B) = 0.45


Hi.

Can u tell me wat is P(AandB)????

Please clear my doubt.

regards,
Rrsnathan.

P(A and B)= probability both events (A,B) occur= P(A)*P(B).

Hope this clear your doubt
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Alternate approach

P(Total) = 1 | P(Event A) = 0.4 | P(Both) = 0.25 (from question stem)

P(Neither) = 1 - P(Either event A or event B) = 1 - 0.6 = 0.4

P(Total) = P(Event A) + P(Event B) - P(Both) + P(Neither)

Substituting values, \(1 = 0.4 + P(Event B) - 0.25 + 0.4\)
-> \(1 = 0.8 - 0.25 + P(Event B)\) -> \(P(Event B) = 1 - 0.55\) = 0.45(Option C)
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shrive555
The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?

A. 0.05
B. 0.15
C. 0.45
D. 0.50
E. 0.55

We can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

So we have:

0.6 = 0.4 + P(B) - 0.25

0.6 = 0.15 + P(B)

0.45 = P(B)

Answer: C
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Could you explain

"If the probability that either event A or event B occurs is 0.6"
meaning 0.4 = P of not A and not B?

Thanks!


AliciaSierra


Using Manhattan book formula
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The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur? (Assume that the probabilities of events A and B occurring are independent of each other.)

A. 0.05
B. 0.15
C. 0.45
D. 0.50
E. 0.55

P(A or B) = P(A) + P(B) - P(A and B)

Substitute the given values
0.6 = 0.4 + P(B) - 0.25
P(B) = 0.45

Answer: C.

sunshineeee
Could you explain

"If the probability that either event A or event B occurs is 0.6"
meaning 0.4 = P of not A and not B?

Thanks!


“A or B occurs” is the opposite of “neither A nor B occurs.” So if P(A or B) = 0.6, then P(not A and not B) = 1 - 0.6 = 0.4.
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If we assume that probability of events A and B occurring are independent of each other ... doesn't that mean that P(A)*P(B)=P(A and B), but we will get a different answer from that approach won't we?
shrive555
The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur? (Assume that the probabilities of events A and B occurring are independent of each other.)

A. 0.05
B. 0.15
C. 0.45
D. 0.50
E. 0.55
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