Question

Mary is a good student. The probability that she studies and passes her test is 3/5. If the probability that she studies is 8/9. What is the probability that she passes given that she studies?
(1 Point)

.8%

5.9%

67.5%

148%

Answer 1

To find the probability that Mary passes given that she studies, we can use conditional probability.

Let:
- \( P(S) \) be the probability that Mary studies.
- \( P(P|S) \) be the probability that Mary passes given that she studies.
- \( P(P \cap S) \) be the probability that Mary studies and passes.

We have:
- \( P(P \cap S) = \frac{3}{5} \)
- \( P(S) = \frac{8}{9} \)

We need to find \( P(P|S) \), which can be calculated using the formula:

\[
P(P|S) = \frac{P(P \cap S)}{P(S)}
\]

Substituting the values we have:

\[
P(P|S) = \frac{\frac{3}{5}}{\frac{8}{9}}
\]

To divide the fractions, we can multiply by the reciprocal:

\[
P(P|S) = \frac{3}{5} \times \frac{9}{8} = \frac{3 \times 9}{5 \times 8} = \frac{27}{40}
\]

Now, to convert the fraction \( \frac{27}{40} \) into a percentage:

\[
\frac{27}{40} = 0.675 = 67.5\%
\]

Thus, the probability that she passes given that she studies is \( 67.5\% \).

The answer is **67.5%**.