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The events A and B are independent. The probability that event A occur

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The events A and B are independent. The probability that event A occur  [#permalink]

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New post 10 Jul 2016, 23:58
2
12
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

47% (01:04) correct 53% (01:09) wrong based on 188 sessions

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The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q

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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 11 Jul 2016, 00:29
2
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q



Probability of A occuring = p , Probability of A NOT occuring = 1-p
Probability of B occuring = q , Probability of B not occurring = 1-q

Probability of atleast of one of A and B occuring = 1-(1-p)(1-q) = p+q -pq

D

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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 11 Jul 2016, 03:37
2
I ll go with C

Probability of A happening and B not happrning- p*(1-q)
Probability of B happening and A not happening- q*(1-p)

Exactly 1 of them happening- p*(1-q)+ q*(1-p) = p+q-2pq
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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 11 Jul 2016, 09:43
1
prashant212 wrote:
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q



Probability of A occuring = p , Probability of A NOT occuring = 1-p
Probability of B occuring = q , Probability of B not occurring = 1-q

Probability of atleast of one of A and B occuring = 1-(1-p)(1-q) = p+q -pq

D



This is not right. When you consider atleast one, it also means you are considering the possibility of both events occuring, which should be excluded as per the question.

So correct would be A occurs, B doesn't occur and B occurs, A doesn't occur = p(1-q) + q(1-p) = p+q-2pq
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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 13 Jul 2016, 08:45
P does and q does not or q does and p does not
p(1-q)+q(1-p),
p+q-2pq
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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 13 Jul 2016, 21:12
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q



Just to confirm, if we had to find the probability that one of the events A and B occurs (omitted the highlighted text)-
it would have been:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = p+ q- pq

Is this correct?
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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 10 Jun 2018, 09:51
Probability of Exactly one of A or B occurring if I write it in Union form:
P(Exactly one occurring) = P(a U b) - P(a n b) = p(a) + p(b) - 2(p(a n b)) = p + q - 2pq(since a and b are independent)
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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 10 Jun 2018, 09:52
Anigr16 wrote:
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q



Just to confirm, if we had to find the probability that one of the events A and B occurs (omitted the highlighted text)-
it would have been:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = p+ q- pq

Is this correct?


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Re: The events A and B are independent. The probability that event A occur  [#permalink]

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New post 12 Aug 2019, 11:50
Bunuel wrote:
The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p − 2pq
B. q − pq
C. p + q − 2pq
D. p + q − pq
E. p + q


Because events A and B are independent, the probability that both A and B occur is the product of their individual probabilities, so we have P(A and B) = pq.

Now, note that the event “A only” means that the part of A that includes both A and B happening is not part of this event. Thus, we have:

P(A only) = P(A) - P(A and B) = p - pq.

Similarly, for the event “B only” we see that

P(B only) = P(B) - P(A and B) = q - pq.

Thus, the probability that exactly one event happens (i.e., A only or B only) is equal to

p - pq + q - pq = p + q - 2pq.

Answer: C
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Re: The events A and B are independent. The probability that event A occur   [#permalink] 12 Aug 2019, 11:50
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