Question

The likelihood that Johan, Julia and Josefin will be delayed in a crucial business meeting are • 0.12 (Johan) • 0.35 (Julia) • 0.02 (Josefin).

a) What is the likelihood that at least one of the people will be delayed?

b) What is the probability that exactly one will be delayed?

Answer 1

(a)

Let A be event that Lohan is delayed.

B be the event Julia is delayed

C be the event Josefin is delayed.

Given:

P(A) = 0.12

P(B) = 0.35

P(C) = 0.02

(a) P(at least one A,B,C will be delayed) = 1 - P(All A,B,C are delayed) = 1 - (0.12 X 0.35 X 0.02) = 1 - 0.00084 = 0.99916

So,

Answer is:

0.99916

(b)

P() = P(A in time) = 1 - 0.12 = 0.88

P() = P(B in time) = 1 - 0.35 = 0.65

P() = P(C in time) = 1 - 0.02 = 0.98

P(Exactly one of A,B,C is delayed) :

P(A delayed and B & C in time) = 0.12 X 0.65 X 0.98 = 0.07644

P(B delayed and A & C in time) = 0.88 X 0.35 X 0.98 = 0.30184

P(C delayed and B & C in time) = 0.88 X 0.65 X 0.02 = 0.01144

So,

P(exactly one of A,B,C delayed) = 0.07644 + 0.30184 + 0.01144 = 0.3897

So,

Answer is:

0.3897