Question

a basketball player is shooting free throws blindfolded. he shoots in groups of 4 shots. assume that it is equally likely that he will hit or miss a shot. design and do a simulation to determine the probability that he will hit at least 75% of his shots within the groups. (hint: use coins.)

Explanation:

Step1: Determine the number of successful shots

Since \(75\%\) of \(4\) shots is \(0.75\times4 = 3\) shots. So, we want to find the probability of hitting \(3\) or \(4\) shots.

Step2: Set up the coin - based simulation

Let heads (\(H\)) represent a hit and tails (\(T\)) represent a miss. Each group of \(4\) coin flips represents a group of \(4\) shots.

Step3: Conduct multiple trials

Conduct, say, \(n = 100\) trials (flip \(4\) coins \(100\) times).
For each trial, count the number of heads.

Step4: Calculate the probability

Count the number of trials (\(m\)) where the number of heads is \(3\) or \(4\). The probability \(P=\frac{m}{n}\).

For example, if after \(100\) trials, the number of times we get \(3\) or \(4\) heads is \(30\), then \(P = 0.3\)

Answer:

The probability is found by conducting the coin - flipping simulation as described above. The value of the probability depends on the number of successful ( \(3\) or \(4\) heads) trials out of the total number of trials conducted. For instance, if in \(n = 100\) trials, \(m = 30\) trials have \(3\) or \(4\) heads, the probability is \(0.3\)