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06 May 2026, 19:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:20) correct
29%
(01:10)
wrong
based on 55
sessions
History
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Not Attempted Yet
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
A. p^2
B. (1 – p)^2
C. 1 – (1 – p)^2
D. (1 – p)^2
E. 1 – p^2
06 May 2026, 20:48
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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
= 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
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07 May 2026, 23:11
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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)
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)
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