If events A and B are independent and each has a probability p of

Question

If events A and B are independent and each has a probability p of occurring, which of the following represents the probability that at least one of these events will occur?

A. p^2
B. (1 – p)^2
C. 1 – (1 – p)^2
D. (1 – p)^2
E. 1 – p^2

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AdarshSambare · Answer

Probability that at least one occurs
= 1 − Probability(neither occurs)
Since A and B are independent:
Probability(A does not occur) = 1 − p
Probability(B does not occur) = 1 − p
So,
Probability(neither occurs)
= (1 − p)(1 − p)
= (1 − p)^2
Therefore,
Probability(at least one occurs)
= 1 − (1 − p)^2
 Answer: C. 1 − (1 − p)^2

BongBideshini · Answer

Both A and B occur =  p^2

At least one of these events will occur
 = p + p- p^2
= 2p − p^2 
This is equal to:
 1 − (1 − p)^2

Ans (C)

MartyMurray · Answer

If events A and B are independent and each has a probability p of occurring, which of the following represents the probability that at least one of these events will occur?

There are four possible outcomes:

- Only A occurs

- Only B occurs

- Both A and B occur

- Neither A nor B occurs

The combined probability of those events is 1.

In all cases but the neither case, at least one of A and B occurs.

So, the probability that at least one will occur is the following:

1 - Probability of Neither

Probability of neither:

(Probability that A does not occur)(Probability that B does not occur) = (1 - p)(1 - p) = (1 – p)^2

Probability that at least one occurs:

1 - (1 – p)^2

A. p^2
B. (1 – p)^2
C. 1 – (1 – p)^2
D. (1 – p)^2
E. 1 – p^2

Correct answer:   C

Kinshook · Answer

If events A and B are independent and each has a probability p of occurring, which of the following represents the probability that at least one of these events will occur?

The probability that neither of them will occur = (1-p)^2

The probability that at least one of them will occur = 1-(1-p)^2

IMO C

ExpertsGlobal5 · Answer

Explanation:

The probability that event A will occur = p
The probability that event B will occur = p
The probability that neither event will occur = (1 – p) x (1 – p) = (1 – p)^2
The probability that at least one of these events will occur = 1 – The probability that neither event will occur = 1 – (1 – p)^2

C is the correct answer choice.

vasu1104 · Answer

P ( A occurs) = p
so P( A not occuring) = 1-p

P(B occurs) = p
P(B not occuring) =1-p

P(none will occur) = 1- p(A not occuring) P(B not occuring)
1- (1-p)(1-p)
1- (1-p)^2

option C

If events A and B are independent and each has a probability p of

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GMAT Problem Solving (PS) Questions

If events A and B are independent and each has a probability p of

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