In basketball, "one-and-one" free throw shooting (commonly called foul shooting) is done as follows: if the player makes the first shot (1 point), he is given a second shot. If he misses the first shot, he is not given a second shot (see the tree diagram).
First
Second
Point
No point
Point
No point
Total
2
1
0
shot
shot
points
Christine, a basketball player, has a 70% foul shot record. (She makes 70% of her foul shots.) Find the probability that, on a given one-and-one foul shooting opportunity, Christine will score no points.
The probability that Christine will score no points is equal to the probability that she will miss her first shot.
Given that Christine has a 70% foul shot record, the probability of missing her first shot is equal to 1 - 0.70 = 0.30.
Therefore, the probability that Christine will score no points is 0.30.
To find the probability that Christine will score no points, we need to calculate the probability that she misses both shots.
Given that Christine has a 70% foul shot record, the probability of making a shot is 0.70, and the probability of missing a shot is 0.30.
So, the probability that Christine makes the first shot is 0.70.
The probability that Christine misses the first shot and makes the second shot is (0.30)(0.70) = 0.21.
The probability that Christine misses both the first and second shots is (0.30)(0.30) = 0.09.
Therefore, the total probability that Christine will score no points is 0.09.
To find the probability that Christine will score no points on a given one-and-one foul shooting opportunity, we need to determine the probability of her missing the first shot.
Given that Christine has a 70% foul shot record, it means she makes 70% of her foul shots and thus will miss 30% of the time.
Therefore, the probability of Christine missing the first shot is 0.30.
Hence, the probability that Christine will score no points on a given one-and-one foul shooting opportunity is 0.30.