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

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Senior Manager
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Joined: 15 Sep 2010
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The probability that event A occurs is 0.4, and the probabil [#permalink]

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26 Dec 2010, 18:47
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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?

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

P(A) = .40
P(A and B) = P(A) * P(B) = .25 ----1
P(A or B) = P (A) + P(B) = .60 -----2

Both 1 & 2 give different results.
1 => P(B) = $$.25/P(A)$$ = 0.62
2=> P(B) = .60 - .40 = .20

whats going wrong ...i don;t know
[Reveal] Spoiler: OA

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26 Dec 2010, 21:42
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P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + P(B) - 0.25
P(B) = 0.45
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Joined: 31 May 2010
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26 Dec 2010, 23:30
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P(AandB) = pA + pB - p(AintersectionB)
0.6= 0.4 + p(B) - 0.25
= 0.45
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Kudos if any of my post helps you !!!

Manager
Status: UC Berkeley 2012
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Location: United States
Concentration: Economics, Finance
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27 Dec 2010, 03:29
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you can state both equations only if they are independent from each other ...
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Location: India
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10 Aug 2013, 05:33
hirendhanak wrote:
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)????

regards,
Rrsnathan.
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10 Aug 2013, 05:59
1
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rrsnathan wrote:
hirendhanak wrote:
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)????

regards,
Rrsnathan.

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

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Senior Manager
Joined: 10 Jul 2013
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10 Aug 2013, 14:10
shrive555 wrote:
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?

0.05
0.15
0.45
0.50
0.55

P(A) = .40
P(A and B) = P(A) * P(B) = .25 ----1
P(A or B) = P (A) + P(B) = .60 -----2

Both 1 & 2 give different results.
1 => P(B) = $$.25/P(A)$$ = 0.62
2=> P(B) = .60 - .40 = .20

whats going wrong ...i don;t know

The only correction you need is to minus...
P(A or B) = P (A) + P(B) - P(A) * P(B) =
or, 0.60 = 0.4 +p(B) - 0.25
so, p(B) = 0.45 (C)

we all make mistake....don't worry about it...
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Director
Joined: 12 Nov 2016
Posts: 788
Re: The probability that event A occurs is 0.4, and the probabil [#permalink]

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12 Oct 2017, 20:30
shrive555 wrote:
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

P(A) = .40
P(A and B) = P(A) * P(B) = .25 ----1
P(A or B) = P (A) + P(B) = .60 -----2

Both 1 & 2 give different results.
1 => P(B) = $$.25/P(A)$$ = 0.62
2=> P(B) = .60 - .40 = .20

whats going wrong ...i don;t know

If A and B are overlapping events then

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

C
Director
Joined: 12 Nov 2016
Posts: 788
Re: The probability that event A occurs is 0.4, and the probabil [#permalink]

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12 Oct 2017, 20:36
shrive555 wrote:
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

P(A) = .40
P(A and B) = P(A) * P(B) = .25 ----1
P(A or B) = P (A) + P(B) = .60 -----2

Both 1 & 2 give different results.
1 => P(B) = $$.25/P(A)$$ = 0.62
2=> P(B) = .60 - .40 = .20

whats going wrong ...i don;t know

Another way of looking at this is that both events are overlapping events- A and B can occur at the same time - this is basically the same as

Total= A + B -both --> is the same thing as saying P(A or B)= P(A) + P(B) -P(A and B)

This is one application of the overlapping set formula to probability
Re: The probability that event A occurs is 0.4, and the probabil   [#permalink] 12 Oct 2017, 20:36
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