Question

An international conference takes place in a metropolitan city. International leaders, scientists and industrialists participate in it.

The organisers of the conference appoint three agencies namely X, Y and Z for the security of the participants. The track record of the success of X, Y and Z in providing security services is 99%, 98.5% and 98% respectively. The organisers assign the responsibility of ensuring the security of 1000 people to agency X, 2000 people to agency Y and 3000 people to agency Z.

At the end of the conference, one participant goes missing from the conference room. What is the probability that the missing participant was placed under the responsibility of the security agency X?

Answer 1

The probability of a person being assigned to each agency X, Y, Z is

P(X) = `1000/(1000 + 2000 + 3000)`

= `1/6`

P(Y) = `2000/(1000 + 2000 + 3000)`

= `1/3`

P(Z) = `3000/(1000 + 2000 + 3000)`

= `1/2`

A be an event of a person going missing under each agency’s responsibility.

`P(A/X) = 1 - 0.99`

= 0.01

`P(A/Y) = 1 - 0.985`

= 0.015

`P(A/Z) = 1 - 0.98`

= 0.02

By Applying Baye’s theorem

`P(X/A) = (P(X) * P(A/X))/(P(X) * P(A/X) + P(Y) * P(A/Y) + P(Z) * P(A/Z)`

= `(1/6 xx 0.01)/(1/6 xx 0.01 + 1/3 xx 0.015 + 1/2 xx 0.02)`

= `(1/600)/(1/600 + 1/200 + 1/100)`

= `(1/600)/((1  +  3  +  6)/600)`

= `(1/600)/(10/600)`

= 0.1