BTGmoderatorDC wrote: ↑Fri Feb 28, 2020 4:32 pm
Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs?
(1) The probability that at least one of events A and B occurs is 0.84.
(2) The probability that event B occurs and event A does not is 0.24.
OA
A
Source: Veritas Prep
Say P(A) = P(B) = x. We have to get the value of x.
Let's take each statement one by one.
(1) The probability that at least one of events A and B occurs is 0.84.
P(A or B) = P(A) + P(B) – P(A & B)
0.84 = x + x – x*x; since A and B are independant events, P(A & B) = P(A)* P(B)
0.84 = x + x – x^2
x^2 – 2x + 0.84 = 0
x^2 – 2x + 1 – 1 + 0.84 = 0
(x – 1)^2 – 0.16 = 0
(x – 1)^2 = 0.16
(x – 1) = ±√(0.16)
x = 1 ± 0.4
x = 0.6 or 1.4. Since x ≤ 1, x ≠ 1.4. So, x = 0.6. Sufficient.
(2) The probability that event B occurs and event A does not is 0.24.
P(B) – P(A & B) = 0.24
x – x^2 = 0.24
x^2 – x + 0.24 = 0
x^2 – x + 1/4 – 1/4 + 0.24 = 0
(x – 1/2)^2 – 0.01 = 0
(x – 0.5)^2 = 0.01
x – 0.5 = 0.1; taking square root
x = 0.4 or 0.6, both values are eligible. No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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