SOLUTION: 5. A basketball player has an overall 60% average of success while shooting free throws. (a) After a foul, she gets ready to make two free throws. One of your students says �she

Question 1009654: 5. A basketball player has an overall 60% average of success while shooting free
throws.
(a) After a foul, she gets ready to make two free throws. One of your students
says �she�s bound to make at least one of the two, since 2�60% > 100%�.
What is the problem with this argument? Explain.
(b) If each successful free throw is worth one point, what is the expected
number of points she�ll make after the foul?
Please help me understand the reasoning behind the solution
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
5. A basketball player has an overall 60% average of success while shooting free
throws.
(a) After a foul, she gets ready to make two free throws. One of your students
says �she�s bound to make at least one of the two, since 2�60% > 100%�.
What is the problem with this argument? Explain.
(b) If each successful free throw is worth one point, what is the expected
number of points she�ll make after the foul?
Please help me understand the reasoning behind the solution

Solution:
A.
First, take note that two tries do not double the probability of success, since probabilities cannot be greater than one. In fact, the sum of probability of all possible outcomes add up to 1. Therefore, we must search for all possible outcomes and determine the probability of each event happening.

B.
We define S=successful throw, and F=unsuccessful throw.
The four possible outcomes are SS, SF, FS, FF.
The corresponding probabilities are:
P(SS)=0.6*0.6=0.36
P(SF)=0.6*0.4=0.24
P(FS)=0.4*0.6=0.24
P(FF)=0.4*0.4=0.16

We define N(x) as the number of points attributed to event x.
The expected number of points are therefore
E(x)=sum P(x)*N(x)
=0.36*2+0.24*1+0.24*1+0.16*0
=1.2
So the expected number of points is 1.2
RELATED QUESTIONS
5. A basketball player has an overall 60% average of success while shooting free throws. (answered by stanbon)

A basketball player has a 70% free throw shooting average, which can be interpreted to... (answered by jim_thompson5910)

A basketball player must score 95 free throws out of 100 in order to qualify for the... (answered by richwmiller)

Supposa a basketball player made 8 of 12 throws. What is her free throw... (answered by solver91311)

A basketball player has a 70% free throw shooting average, which can be interpreted to... (answered by scott8148,stanbon)

Jill and Jack play basketball. In the first game, Jill had a foul shot average of 0.60... (answered by stanbon)

A basketball player shooting 49% from the line attempts 11 free throws in a game. What is (answered by rothauserc)

The ratio of a basketball player completed free throws to attempted free throws is 9 to... (answered by fractalier)

The function f(x) = 1 + 1.5ln(x+1) models the average number of free-throws a basketball... (answered by ankor@dixie-net.com)