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If events E and F are independent and each has a probability p of occurring, which of the following represents the probability that E will occur but F will not occur?
A) p^2
B) 1-p^2
C) p^2-1
D) p^2-p
E) p-p^2
A) p^2
B) 1-p^2
C) p^2-1
D) p^2-p
E) p-p^2
28 Jun 2023, 08:13
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rakman123
If events E and F are independent and each has a probability p of occurring, which of the following represents the probability that E will occur but F will not occur?
A) p^2
B) 1-p^2
C) p^2-1
D) p^2-p
E) p-p^2
A) p^2
B) 1-p^2
C) p^2-1
D) p^2-p
E) p-p^2
Event E
- Probability of occurring = p
- Probability of not occuring = 1-p
Event F
- Probability of occurring = p
- Probability of not occuring = 1-p
Required Probability = P(Event E occurring) * P(Event F not occurring)
= p * (1-p)
\(= p - p^2\)
Option E
General Discussion
07 Aug 2023, 03:54
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Bunuel
If events E and Fare independent and each has probability p of occurring, which of the following represents the probability that E will occur but F will not occur?
A. p^2
B. 1 - p^2
C. p^2 - 1
D. p^2 - p
E. p - p^2
A. p^2
B. 1 - p^2
C. p^2 - 1
D. p^2 - p
E. p - p^2
If events E and F are independent, then E and not-F are independent as well. (Also, not-E and F are independent, and not-E and not-F are independent.)
P(E and not-F) = P(E) × P(not-F) = p × (1 – p) = p – p^2
Answer: E
