posted by Anthony on .
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
They are asking for a long term average. The table shows the results of 100 consecutive shots, which may or may not be representativeof a long term average.
The probability of making two in a row is (0.4)^2 = 0.16, over the long term, unless there is a tendency for players to have "hot streaks" and "cold streaks". These should not happen with a random number generator. There is interesting data on the "hot hand" theory in basketball, but it is not convincing either way.
There are 99 pairs of consecutive shots in the table. There are 17 times that 2 shots in a row are made. Count them