Question

A number wheel has 16 equally likely spaced slots numbered 1 to 16. Jake bets $1 on one of the numbers and wins $25 when the wheel lands on his number. If the wheel stops at another number, he would have lost money. The random variable X assigns $25 to the wheel landing on the chosen number and -$1 to having the wheel land on any other number. WHAT IS THE EXPECTED VALUE OF THE NUMBER ON THE WHEEL? ($0.63, $0.78, $0.32, $0.17)

Answer 1

Answer:

$0.63

Explanation:

We were given that:

The wheel has 16 slots

Jake bets $1 on one of the slots & wins $25

If the wheel lands on any other slot, he will lose $1

The expected value is given by:

$\begin{gathered} E.V.=(\frac{1}{16}\times25)+(\frac{15}{16}\times-1) \\ E.V.=\frac{25}{16}-\frac{15}{16} \\ E.V.=\frac{10}{16} \\ E.V.=0.625\approx0.63 \\ E.V.=0.63 \end{gathered}$

Therefore, the expected value is $0.63