Question

3 fill in the blank 20 points roberto is the owner of a car dealership. he is assessing the success rates of his top three sales people in order to offer one of them a promotion. over two months, for each attempted sale, he records whether the sales person made a successful sale or not. the results are shown in the table below. write all answers as fractions in simplest form. | | successful | unsuccessful | |---|---|---| | becky | 6 | 6 | | raul | 4 | 5 | | darrell | 6 | 9 | a) find ( p(\text{unsuccessful} | \text{raul}) ) type your answer.. b) find ( p(\text{successful} | \text{becky}) ) type your answer..

Explanation:

Part A:

Step 1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). For \( P(\text{Unsuccessful} | \text{Raul}) \), we consider only Raul's data. The number of trials for Raul is the total of his successful and unsuccessful sales.

Step 2: Calculate Total Trials for Raul

Raul's successful sales: \( 4 \), unsuccessful sales: \( 5 \). Total trials \( n = 4 + 5 = 9 \).

Step 3: Calculate Probability

The number of unsuccessful sales for Raul is \( 5 \). So \( P(\text{Unsuccessful} | \text{Raul}) = \frac{\text{Unsuccessful for Raul}}{\text{Total for Raul}} = \frac{5}{9} \).

Part B:

Step 1: Recall Conditional Probability Formula

For \( P(\text{Successful} | \text{Becky}) \), we use Becky's data.

Step 2: Calculate Total Trials for Becky

Becky's successful sales: \( 6 \), unsuccessful sales: \( 6 \). Total trials \( n = 6 + 6 = 12 \).

Step 3: Calculate Probability

The number of successful sales for Becky is \( 6 \). So \( P(\text{Successful} | \text{Becky}) = \frac{\text{Successful for Becky}}{\text{Total for Becky}} = \frac{6}{12} = \frac{1}{2} \).

Answer:

A) \(\frac{5}{9}\)
B) \(\frac{1}{2}\)