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Suppose a basketball player has made

204 out of 409 free throws. If the player makes the next 3 free throws, I will pay you
$17. Otherwise you pay me $4.
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. 

Step 2 of 2:

If you played this game 921 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.
User Ainsausti
by
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1 Answer

1 vote

Solution-

The probability of making a single shot is,


P(x)=(204)/(409)

The probability of making 3 shot will be,


P(x)=((204)/(409))^3=0.1241

The probability of not making 3 shot is,


P'(x)=1-P(x)=1-((204)/(409))^3=1-0.1241=0.8759

The expected gain for the basketball player will be,

= (Probability of making 3 shots) × ($17) + (Probability of NOT making 3 shots) x (-$4)


=(0.1241)* (17)+(0.8759)* (-4)


=2.1097-3.5036


=-1.3939


=-1.39

So the basketball player is expected to lose, on average, $1.39

If he played this game 921 times how much would you expect to win or lose


=-1.39* 921=-1280.19

So the basketball player is expected to lose $1280.19, if he plays this game 921 times.

User Xavier Bouclet
by
8.6k points