In an experiment, college students were given either four quarters or a $$1$ bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts $($a$)$ through $($c$)$ below.

$\backslash$table$[[,$Purchased Gum,Kept the Money$],[$Students Given Four Quarters,$31,14],[$Students Given a $$1$ Bill,$15,35]]$

a$.$ Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

The probability is

$($Round to three decimal places as needed.$)$

b$.$ Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

The probability is

$($Round to three decimal places as needed.$)$

c$.$ What do the preceding results suggest?

A$.$ A student givin four quarters is more likely to have kept the money.

B$.$ A student given four quarters is more likely to have kept the money than a student given a $$1$ bill.

C$.$ A student given four quarters is more likely to have spent the money.

D$.$ A student given four quarters is more likely to have spent the money than a student given a $$1$ bill.