Question

A Game of Thrones fan predicts there is a 70% chance that her favorite character will survive the next season and a 75% chance that her second favorite character will die. There is also a 16% chance that both characters will die. What’s the probability that the second character will die given that the first character dies? What kind of probability is this called?

Answer 1

Answer:

• The probability that the second favorite character will die given that the first favorite character dies is 0.53

• This kind of probability is called conditional probability

Explanation:

Name the events and their probabiities:

• Event  A: her favorite character will survive, so P (A) = 0.70

• Event B: her her second favorite character will die, so P(B) = 0.75

• Both characters will die ⇒ P (B and not A) = 0.16

You want to find P (B | not A).

That is the probability of the succes B (the second favorite character will die) given other event (not A or the first favorite character dies) is certain (it happens) and that is called conditional probability.

• P (not A) is the complement probability of A, so P (not A) = 1 - P(A) = 1 - 0.7 = 0.3

So, you have P(B), P(not A) and want to find P (B | not A)

The definition of conditional probability is:

• P (X | Y) = P (X and Y) / P (Y)

So, replacing with our terms, we get:

• P ( B | not A) = P (B and not A) / P (not A) = 0.16 / 0.3 ≈ 0.53