Question

If A and B are independent events and P(A) and P(B) are both greater than 1/2

then P(A and B) is greater than 1.
A always
B not enough information provided to answer the question
C never
D sometimes

Answer 1

P(A and B) is greater than 1 is never happened ⇒ C

Explanation:

Two events are independent if the result of the second event is not affected by the result of the first event

If A and B are independent events, the probability of both events is the product of the probabilities of the both events P (A and B) = P(A) · P(B)

∵ The probability of any event is less than 1

∵ P(A) < 1

∵ P(A) >
`(1)/(2)`

- That means P(A) is greater than half and less than 1

∴
`(1)/(2)` < P(A) < 1

∵ P(B) < 1

∵ P(B) >
`(1)/(2)`

- That means P(B) is greater than half and less than 1

∴
`(1)/(2)` < P(B) < 1

∵ P(A and B) = P(A) . P(B)

- Remember the product of any fractions less than 1 is less than 1

∴
`(1)/(4)` < P(A) . P(B) < 1

- That means any expression equals to P(A) . P(B) must be greater

than
`(1)/(4)` and less than 1

∴
`(1)/(4)` < P(A and B) < 1

∴ P(A and B) is greater than 1 is never happened