QuestionFind the probability that a seasoned employee has a credit card, given the table: $P(\text{Credit Card | Seasoned}) = \frac{27}{92}$ . Round to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The total number of employees is125. . The number of seasoned employees is92.
3. The number of seasoned employees with a credit card is27.
4. We are asked to find the conditional probability of an employee having a credit card given that they are a seasoned employee.

STEP 2

The formula for conditional probability is $(A|B) = \frac{(A \cap B)}{(B)}$ where- $(A|B)$ is the probability of event A occurring given that event B has occurred, - $(A \cap B)$ is the probability of both events A and B occurring, - $(B)$ is the probability of event B occurring.

STEP 3

In this case, event A is an employee having a credit card and event B is the employee being seasoned. So we need to find $(A|B)$ , the probability of an employee having a credit card given that they are a seasoned employee.

STEP 4

First, we find $(A \cap B)$ , the probability of both events A and B occurring. This is the probability of a seasoned employee having a credit card. We find this by dividing the number of seasoned employees with a credit card by the total number of employees.
$(A \cap B) = \frac{Number\, of\, seasoned\, employees\, with\, a\, credit\, card}{Total\, number\, of\, employees}$

STEP 5

Substitute the given values into the equation.
$(A \cap B) = \frac{27}{125}$

STEP 6

Calculate $(A \cap B)$ .
$(A \cap B) = \frac{27}{125} =0.216$

STEP 7

Next, we find $(B)$ , the probability of event B occurring. This is the probability of an employee being seasoned. We find this by dividing the number of seasoned employees by the total number of employees.
$(B) = \frac{Number\, of\, seasoned\, employees}{Total\, number\, of\, employees}$

STEP 8

Substitute the given values into the equation.
$(B) = \frac{92}{125}$

STEP 9

Calculate $(B)$ .
$(B) = \frac{92}{125} =.736$

STEP 10

Now we can find $(A|B)$ , the probability of an employee having a credit card given that they are a seasoned employee. We find this by dividing $(A \cap B)$ by $(B)$ .
$(A|B) = \frac{(A \cap B)}{(B)}$

STEP 11

Substitute the calculated values into the equation.
$(A|B) = \frac{0.216}{0.736}$

STEP 12

Calculate $(A|B)$ and round to two decimal places.
$(A|B) = \frac{0.216}{0.736} =0.29$ The probability of an employee having a credit card given that they are a seasoned employee is0.29.

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