# Identifying dependent pairs of events

Which of the following pairs of events are dependent?

options:

A)Drawing a heart from a deck of cards, replacing it, and then drawing another heart.

B)Tossing three coins at the same time and getting tails on all three.

C)Randomly choosing a captain and an assistant captain from a team of 18 players.

D)Choosing a class president from one group of students and a vice-president from a different group of students.

My work:

First let's define what a dependent event is: Two events are dependent if the outcome of the first event affects the outcome of the second event, so that the probability is changed. So out of those four choices (A,B,C,D) the correct choice that displays the dependent event is A) Drawing a heart from a deck of cards, replacing it, and then drawing another heart.

Is this choice correct?

• is this correct? Jun 9, 2020 at 19:39

No, replacing the card makes the deck return to its original state with no change in probability whatsoever. The correct choice should be (c), because for instance the probability of Player $$1$$ being vice captain is $$\frac{1}{18}$$ only if he/she is not chosen as captain, in which case the probability of him/her being vice captain will be zero.