Question

1. mr. zachary posts review assignments on the betamath website for his students. on his last test, 49% of his students used betamath and passed. overall, 68% of his students used betamath. approximately what percentage of mr. zacharys students passed, given that they used betamath?

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B)=\frac{P(A\cap B)}{P(B)} \), where \( A \) is the event of passing and \( B \) is the event of using Betamath.

Step2: Identify Given Probabilities

We know that \( P(A\cap B) = 0.49 \) (49% of students used Betamath and passed) and \( P(B)=0.68 \) (68% of students used Betamath).

Step3: Calculate the Conditional Probability

Substitute the values into the formula: \( P(A|B)=\frac{0.49}{0.68}\approx0.7206 \), which is approximately 72%.

Answer:

Approximately 72%