Chapter 13.6, Problem 39SPR

To determine

To determine whether the events are independent or dependent. Also find probability.

Answer to Problem 39SPR

Events are dependent.

Probability is $\frac{15}{2652}$ or 0.5%

Explanation of Solution

Given information :

A king is drawn, without replacement, from a standard deck of 52 cards. Then, a second king is drawn.

If any event A does not affect the outcome of an event B, then event A and B are independent whereas if it affects then the events are dependent.

As there is no replacement therefore probability of first event will affect the probability of second event. Hence the events are dependent.

Here total possibilities are 52.

Probability of getting a king is $\frac{4}{52}$

Then without replacement, getting a king again is $\frac{4}{52}\cdot \frac{3}{51}=\frac{15}{2652}$ or 0.5%

(As one king is already drawn, left are 51 total cards and 3 total kings)