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The number of students who were given four quarters as well as a $1 bill is tabulated based on whether they kept the money or spent it.

As the name suggests, the conditional probability of an eventis the probability of the event happening subject to a condition that an event has already occurred. It has the following formula:

Let A be the event of selecting a student who was given four quarters.

Let B be the event of selecting a student who was given a $1 bill.

Let C be the event of selecting a student who spent the money (purchased gum).

Let D be the event of selecting a student who kept the money.

The following table shows the necessary totals:

a.

The total number of students is equal to 89.

The number of students who were given four quarters is equal to 43.

The probability of selecting a student who was provided four quarters is given by:

$P\left(A\right)=\frac{43}{89}$

The number of students who were given four quarters and spent the money is equal to 27.

The probability of selecting a student who was provided four quarters and spent the money is given by:

$P\left(AandC\right)=\frac{27}{89}$

The probability of selecting a student who spent the money, given that he/she was provided four quarters, is computed as follows:

$$\begin{gathered} P\left(C|A\right)=\frac{P\left(AandC\right)}{P\left(A\right)} \\ =\frac{\frac{27}{89}}{\frac{43}{89}} \\ =\frac{27}{43} \\ =0.628 \end{gathered}$$

Therefore, the probability of selecting a student who spent the money, given that he/she was provided four quarters, is equal to 0.628.

b.

The number of students who were given four quarters and kept the money is equal to 16.

The probability of selecting a student who was given four quarters and kept the money is given by:

$P\left(AandD\right)=\frac{16}{89}$

The probability of selecting a student who kept the money, given that he/she was provided four quarters, is computed as follows:

$$\begin{gathered} P\left(D|A\right)=\frac{P\left(AandD\right)}{P\left(A\right)} \\ =\frac{\frac{16}{89}}{\frac{43}{89}} \\ =\frac{16}{43} \\ =0.372 \end{gathered}$$

Therefore, the probability of selecting a student who kept the money, given that he/she was provided four quarters, is equal to 0.372.

c.

As the probability of selecting a student who spent the money is greater than that of a student who kept the money when offered with four quarters, it can be concluded that students tend to spend money rather than keep it.

Thus, it is suggestive that there is a significantly higher tendency to purchase gum rather than keep the money if offered four quarters.