Questions: III Homework Chapter 4.3 Homework Introductory Statistics - MATH-1530-M9) 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. Students Given Four Quarters Students Given 1 Bill Purchased Gum 27 12 Kept the Money 28 29 a. Find the probability of randomly selecting a student who spent the money given that the student was given four quarters. (Round to three decimal places as needed.) The probability is b. Find the probability of randomly selecting a student who was given a 1 bill given that the student kept the money. (Round to three decimal places as needed.) The probability is Question 15: 4.3:14 H/V Score: 86.21%, 28 of 29 points Points: 2 of 3 Save Alyse Crawford 10/27/23 5:13 PM

Solution Steps

a. To find the probability of a student spending the money given they were given four quarters, use the formula for conditional probability: \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). Here, \( A \) is the event that a student spent the money, and \( B \) is the event that a student was given four quarters. Calculate the number of students who spent the money out of those who were given four quarters and divide by the total number of students given four quarters.

b. To find the probability of a student being given a $1 bill given they kept the money, again use the conditional probability formula. Here, \( A \) is the event that a student was given a $1 bill, and \( B \) is the event that a student kept the money. Calculate the number of students who kept the money out of those who were given a $1 bill and divide by the total number of students who kept the money.

The total number of students given four quarters is calculated as follows: \[ \text{Total Given Quarters} = 27 + 28 = 55 \]

The probability of a student spending the money given that they were given four quarters is: \[ P(\text{Spent} | \text{Quarters}) = \frac{27}{55} \approx 0.491 \]

The total number of students given a $1 bill is: \[ \text{Total Given Dollar} = 12 + 29 = 41 \]

The probability of a student being given a $1 bill given that they kept the money is: \[ P(\text{Dollar} | \text{Kept}) = \frac{29}{57} \approx 0.509 \]

Final Answer