A basketball player has a 40% shooting average from the free-throw line. If she takes two free throws, estimate the probability that she will make both of them. Use the following list of digits which was taken from a table of random numbers. Let the digits 0-3 represent a made free throw and let the digits 4-9 represent a miss. Start at the top left of the table and move all the way across to the right of the table before moving down to the next row.
52052 24004 03845 11507
27510 33761 86563 61729
48061 59412 79969 11339
27324 72723 22406 86253
29970 95877 70975 99120
I got 46 shots made and 54 missed. Now what?
To estimate the probability that the basketball player will make both free throws, we can use the shooting average of 40%. This means that out of 100 free throws, the player is expected to make 40 of them.
Since we have 100 digits in the table, we can consider each digit as representing a free throw. The digits 0-3 represent a made free throw, and the digits 4-9 represent a missed free throw.
Now, let's count the number of made and missed free throws from the given table of digits. You have already counted 46 made shots and 54 missed shots.
To estimate the probability of making both free throws, we need to calculate the probability of making one free throw and multiply it by itself since we want to find the probability of making both of them.
The probability of making one free throw is the shooting average of 40%, which can be expressed as 0.4. Therefore, the probability of making both free throws can be estimated as:
Probability of making both free throws = (Probability of making one free throw) x (Probability of making one free throw)
= 0.4 x 0.4
= 0.16
So, the estimated probability that the basketball player will make both free throws is 0.16, or 16%.