Chapter 13.5, Problem 7PPS

To determine

To determine whether the given events are independent or dependent, and find probability.

Answer to Problem 7PPS

The events are dependent.

Probability is $\frac{1}{221}.$

Explanation of Solution

Given information:

An ace is drawn, without replacement, from a deck of 52 cards. Then, a second ace 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.

Here we can determine that the events are dependent. As there is no replacement probability of first event affects the probability of second event.

Let us take event A= An ace is drawn.

Hence P(A) = $\frac{4}{52}=\frac{1}{13}$

Similarly let event B= second ace is drawn from the remaining cards.

One ace and one card is already taken,

Hence P(B) = $\frac{3}{51}=\frac{1}{17}$

Therefore,

  $P\left(A\text{ and }B\right)=\frac{1}{13}\times \frac{1}{17}=\frac{1}{221}$