The probability that event A occurs is 0.4, and the probabil

Question

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

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

hirendhanak · Accepted Answer

P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + P(B) - 0.25
P(B) = 0.45

AliciaSierra · Answer

Using Manhattan book formula

saurabhgoel · Answer

P(AandB) = pA + pB - p(AintersectionB)
0.6= 0.4 + p(B) - 0.25
= 0.45

e1s · Answer

you can state both equations only if they are independent from each other ...

rrsnathan · Answer

Hi.

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

Please clear my doubt.

regards,
Rrsnathan.

Zarrolou · Answer

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

Hope this clear your doubt

pushpitkc · Answer

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)

ScottTargetTestPrep · Answer

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

sunshineeee · Answer

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!

Bunuel · Answer

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

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.

“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.

pussycat123 · Answer

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?

The probability that event A occurs is 0.4, and the probabil

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