Question

Suppose a basketball player has made 191 out of 325 free throws. If the player makes the next 2 free throws, I will pay you $11. Otherwise you pay me $7. Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

Answer:

So this basketball player is going to loose (-$3.35)

Step-by-step explanation:

$\textrm{Probability of making a single shot is} = P(x)=\dfrac{191}{325}\\\textrm{ Probability of making 2 shots }= P(x)=\left(\dfrac{191}{325}\right)^3= 0.203\\\textrm{ Probability of not making 2 shots}\\=P'(x)=1-P(x)=1-\left(\dfrac{191}{325}\right)^3=1-0.203=0.797$

Expected gain of basketball player will get

=  (probability of making 2 shorts) $\times$ $11 + {probability of making 2 shorts)

$\times$ (-$7}

= 0.203 $\times$ $11 + 0.797 $\times$ (-$7) =( -$3.346)

So this basketball player is going to loose (-$3.35)