Chapter 12.4, Problem 15PPS

a.

To determine

Find the expected value of a card drawn from a standard deck.

Answer to Problem 15PPS

  $7$

Explanation of Solution

Given information:

In a standard deck of $52$ cards, there are 4 different suits.

If $jacks=11,queens=12,kings=13andace$

Calculation:

Deck of $52$ cards, has4 different suits.

  $\begin{array}{l}p\left(1\right)=p\left(2\right)\mathrm{....}=p\left(13\right)=\frac{1}{13}\\ sothe\exp ectedvalueofthecard,\\ E\left(card\right)={\displaystyle \sum _{i=1}^{13}i\cdot p\left(i\right)}\\ =7\end{array}$

Hence, expected value is $7$ .

b.

To determine

Find the expected number of spades.

Answer to Problem 15PPS

  $2$

Explanation of Solution

Given information:

In a standard deck of $52$ cards, there are 4 different suits.

If you are dealt $7$ cards.

Calculation:

Deck of $52$ cards, has4 different suits.

  $\begin{array}{l}p\left(spade\right)=\frac{1}{4}\\ E\left(spade\right)=7.p\left(spade\right)\\ =7\times \frac{1}{4}\\ =1.75\\ soitconsideredas2\end{array}$

Hence, expected value spade is $2$ .