91影视

The number of students who were given a $1 bill and four quarters is tabulated.

They are further divided into two categories: students who purchased gum and students who kept the money.

The conditional probability of an eventis computed with reference to a prior event that occurred in the past. It has the following formula:

$P\left(B|A\right)=\frac{P\left(AandB\right)}{P\left(A\right)}$

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.

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 89.

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

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

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

The number of students who were given four quarters and kept the money is 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 given 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 given four quarters, is equal to 0.372.

b.

The total number of students is 89.

The number of students who were given a $1 bill is 46.

The probability of selecting a student who was given a $1 bill is given by:

$P\left(B\right)=\frac{46}{89}$

The number of students who were given a $1 bill and kept the money is 34.

The probability of selecting a student who was given a $1 bill and kept the money is given by:

$P\left(BandD\right)=\frac{34}{89}$

The probability of selecting a student who kept the money, given that he/she was given a $1 bill, is computed as follows:

$$\begin{gathered} P\left(D|B\right)=\frac{P\left(BandD\right)}{P\left(B\right)} \\ =\frac{\frac{34}{89}}{\frac{46}{89}} \\ =\frac{34}{46} \\ =0.739 \end{gathered}$$

Therefore, the probability of selecting a student who kept the money, given that he/she was given a $1 bill, is equal to 0.739.

c.

The probability of selecting a student who kept the money, given that the student was given a $1 bill, is 0.739. It is much greater than the probability of selecting a student who kept the money when provided with four quarters (0.372).

Thus, the students who received a $1 bill have a greater tendency of keeping the money as compared to the students who received four quarters.

The results suggest higher chances of a student keeping the money when given a $1 bill.