Question

. A person has two meetings schedule in a day. The probability she is late for the first

meeting is 0.4, the probability she is late for the second is 0.5, and the probability

she is late for both meetings is 0.3.

Please explain with where each number comes from and the meaning of formulas used if possible, thank you!

a) Is the event that she is late for the first meeting independent of the event that

she is late for the second meeting? Explain

b) Are the two events disjoint? Explain

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

d) What is the probability that she is not late for either one (she is late for neither)?

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

f) Find the probability that she is late for the first meeting if she was late for the second meeting?

Answer 1

Solution:

Let us define some events as follows:

A : Person is late for first meeting

B : Person is late for second meeting

Then, P(A ∩ B) : Person is late for both the meetings

Given that, P(A) = 0.4, P(B) = 0.5 and  P(A ∩ B) = 0.3

a) If A and B are two independent events then,

P(A ∩ B) = P(A).P(B)

P(A).P(B) = 0.4 × 0.5 = 0.20

P(A ∩ B) = 0.3

i.e.  

Hence, the event that she is late for the first meeting is not independent of the event that she is late for the second meeting.

b) If A and B are two mutually disjoint events then,

P(A ∩ B) = 0

Since, we have P(A ∩ B) = 0.3

Hence, the two events are not disjoint events.

c) We have to obtain probability that she will is late for at least one meeting.

P(late for at least one meeting) = P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 0.4 + 0.5 - 0.3

P(A ∪ B) = 0.6

The probability that she is late for at least one meeting is 0.6.

d) We have to obtain the probability that she is late for neither meeting.

P(late for neither meetings) = 1 - P(late for at least one meeting)

P(late for neither meetings) = 1 - 0.6 = 0.4

The probability that she is late for neither meetings is 0.4.