Question

“Knives Out” is an American murder-mystery film released in 2019. In the film, a wealthy crime novelist is murdered in his home. The plot of the movie is to find the murderer. Before any evidence is gathered, all family members and persons employed by the murder victim are considered as suspects. There are 14 such people in total. Only 1 person out of the 14 suspects is the murderer. The technology company Apple permits its products to be used in films, but bad characters can’t have an iPhone onscreen. That is, the murderer cannot be seen in the film using an Apple iPhone. Seven out of the fourteen murder suspects are observed in the film to be using an Apple iPhone. It is estimated that 45% of the American population use an Apple iPhone. The murder victim’s eldest daughter, Linda, did not murder her father. What is the probability that Linda uses an Apple iPhone?

Answer 1

Answer:

Here A alone be the occasion that an arbitrary individual utilized Apple Iphone.

M alone be the occasion that an arbitrary individual is a killer

Let M' be the occasion that an arbitrary individual isn't a killer or utilization an Apple Iphone

P(M) = One out of 14 suspects is a killer

i.e.,

= 1/14

P(M') = 1 - P(M)

= 1 - 1/14

= 13/14

P(A) = 5/14

Given that, the individual uses an Apple Iphone, likelihood that he/she is a killer

= P(M | A)

= 0

P(M' | A) = 1 - P(M | A)

= 1 - 0

= 1

Given that Linda isn't a killer, likelihood that Linda uses and Apple Iphone

= P(A | M')

= P(M' | A)*P(A) / P(M') (since by using Bayes hypothesis)

substitute values

= 1 * (5/14)/(13/14 )

= 5/14 * 14/13

= 5/13

= 0.3846