Step 1 :The problem is asking for the conditional probability of a student keeping the money given that the student was given four quarters. From the table, we can see that the total number of students given four quarters is 26 + 16 = 42.
Step 2 :Out of these 42 students, 16 students kept the money.
Step 3 :Therefore, the probability of a student keeping the money given that they were given four quarters is calculated as \(\frac{16}{42}\).
Step 4 :Using a calculator, we find that \(\frac{16}{42}\) is approximately 0.38095238095238093.
Step 5 :Rounding to three decimal places, we get 0.381.
Step 6 :Final Answer: The probability of randomly selecting a student who kept the money, given that the student was given four quarters is approximately \(\boxed{0.381}\).