Questions: Here is probability data on a random sample of students who have enrolled in a Business-related Math course... PASS FAIL Withdrew TOTAL -------------------------------------- Calculus .36 .05 .03 .44 Statistics .45 .04 .07 .56 TOTAL .81 .09 .10 1 Compute the probability of passing the course given that the course taken was statistics. P(pass stat) = P(pass ∩ stat) / P(stat)

Solution Steps

To find the probability of passing the course given that the course taken was statistics, we use the conditional probability formula: \( P(\text{pass} \mid \text{stat}) = \frac{P(\text{pass} \cap \text{stat})}{P(\text{stat})} \). From the data, \( P(\text{pass} \cap \text{stat}) \) is the probability of passing statistics, and \( P(\text{stat}) \) is the total probability of taking statistics.

We are given the following probabilities from the data:

• \( P(\text{pass} \cap \text{stat}) = 0.45 \)
• \( P(\text{stat}) = 0.56 \)

To find the conditional probability \( P(\text{pass} \mid \text{stat}) \), we use the formula: \[ P(\text{pass} \mid \text{stat}) = \frac{P(\text{pass} \cap \text{stat})}{P(\text{stat})} \]

Substituting the known values into the formula: \[ P(\text{pass} \mid \text{stat}) = \frac{0.45}{0.56} \]

Calculating the above expression gives: \[ P(\text{pass} \mid \text{stat}) \approx 0.8036 \]

Final Answer