Question

Consider the following scenario: P(E) = 0.4, P(F) = 0.5

a. Find P(E or F) if E and F are disjoint

b. Find P(E or F) if E and F are independent

Answer 1

Part (a)

The term "disjoint" is the same as "mutually exclusive".

If events E and F are disjoint, then we know that P(E and F) = 0. In other words, the two events have nothing in common. Therefore, it's impossible for them both to occur simultaneously.

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = 0.4 + 0.5 - 0

P(E or F) = 0.9

Answer: 0.9

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Part (b)

If events E and F are independent, then P(E and F) = P(E)*P(F).

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = P(E) + P(F) - P(E)*P(F)

P(E or F) = 0.4 + 0.5 - 0.4*0.5

P(E or F) = 0.4 + 0.5 - 0.2

P(E or F) = 0.9 - 0.2

P(E or F) = 0.7

Answer: 0.7