Chapter 5.1, Problem 4E

(a)

To determine

To explain what does this probability means.

Explanation of Solution

The probability $\frac{88}{1000}$ given in the question means that out of $1000$ hands of poker containing a pair, we expect about $88$ of these hands to contain a four of a kind. This is the meaning of the probability given in the question for the variety of poker games Texas hold.

(b)

To determine

To explain why doesn’t this probability say that if you play $1000$ such hands, exactly $88$ will be four of a kind.

Explanation of Solution

This probability doesn’t say that if you play $1000$ such hands, exactly $88$ will be four of a kind because it is also possible that there will be $87\text{ or }89$ four of a kinds out of the $1000$ such hands. The amount of four of a kinds is expected to be close to $88$ , but is not necessarily exactly $88$ hands.