5. A person has two meetings scheduled in a day. The probability she is late for

Question

5. A person has two meetings scheduled in a day. The probability she is late for the first meeting is (.4) , the probability she is late for the second is (.5), and the probability she is late for both meetings is (.3).

a) Is the event that she is late for the first meeting independent of the event that she is late for the second meeting? yes or no

b) Are the two events disjoint (mutually exclusive)?

c) What is the probability she is late for at least one meeting?

d) What is the probability she is not late for both meetings?

e) What is the probability she is late for the first meeting if she was late for the second meeting?

Explanation / Answer

a)No, the event that she is late for the first meeting is not independent of the event that she is late for the second meeting, as P(F)*P(S)=0.4*0.5=0.20

But, P(F and S)=0.3 which is not equal to P(F)*P(S).

b)The two events F and S are not mutually exclusive as P(F and S) is not equal to zero.

d)The probability she is not late for both meetings is: 1-P(F and S)’=1-0.3=0.7

e)The probability she is late for the first meeting if she was late for the second meeting is:

P(F given S)=P(F and S)/P(S)

=0.3/0.5

=0.6

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