Question

Confusion of the Inverse Using the same events F and H described in Exercise 3, describe confusion of the inverse.

Short answer

The confusion of the inverse arises when $P\left(H|F\right)$is considered equal to $P\left(F|H\right)$which are the probabilities of two different events.

• $P\left(H|F\right)$is the probability of selecting a high school classmate, given that she is a female friend.

• $P\left(F|H\right)$is the probability of selecting a female friend, given that he/she is a high school classmate.

Step-by-step solution

Given information

Refer to exercise 3, where a random Facebook friend is selected. H is the event of selecting a high school classmate, while F is the event of selecting a female friend.

Define conditional probability 

Let A and B be two events.

Given that A has already occurred, the probability that B occurs is called theconditional probability of B given A. It has the notation $P\left(B|A\right)$.

When $P\left(B|A\right)$is considered the same as $P\left(A|B\right)$, it is called the confusion of the inverse. In general,$P\left(B|A\right)\ne P\left(A|B\right)$ .

Confusion of the inverse with reference to the given events

The two events H and F are defined as the event of selecting a high school classmate and event of selecting a female friend, respectively.

As per the definition of conditional probability, $P\left(H|F\right)$is the probability of selecting a high school classmate, given that the friend is a female, whereas $P\left(F|H\right)$is the probability of selecting a female friend given that he/she is a high school classmate.

The confusion of the inverse states the fact that$P\left(H|F\right)$ is considered equal to$P\left(F|H\right)$.