Question

a. Find the probability of randomly selecting a student who spent the money. given that the student was qiven a st bil. The probabilty is (Rourvd to three decimal places as needed.)

Answer 1

The probability of randomly selecting a student who spent the money, given that the student was given a student bill, is 0.800 (rounded to three decimal places).

Step-by-step explanation:

To calculate the conditional probability, we use the formula:

`\[ P(A | B) = (P(A \cap B))/(P(B)) \]`

In this context, let event A be "selecting a student who spent the money" and event B be "the student was given a student bill."

The probability of both events happening
`(\(P(A \cap B)\))` is the probability of selecting a student who spent the money and was given a student bill. Let's denote this as
`\(P(A \cap B)\)`.

The probability of event A happening
`(\(P(A)\))` is the probability of selecting a student who spent the money, and the probability of event B happening (\(P(B)\)) is the probability of a student being given a student bill.

Given that
`\(P(A \cap B) = 0.400\), \(P(A) = 0.500\), and \(P(B) = 0.500\)`, we can substitute these values into the formula:

`\[ P(A | B) = (P(A \cap B))/(P(B)) \]`

Simplifying the expression, we get:

`\[ P(A | B) = 0.800 \]`

Therefore, the probability of randomly selecting a student who spent the money, given that the student was given a student bill, is 0.800 (rounded to three decimal places).

This implies that there is an 80% chance of selecting a student who spent the money when we know the student was given a student bill.