6 There is a 25% chance that Claire will have to work tonight and cannot study for the big math test. If Claire studies, then she has an 80% chance of earning a good grade. If she does not study, she only has a 30% chance of earning a good grade. a. Draw a diagram to represent this situation. b. Calculate the probability of Claire earning a good grade on the math test. c.If Claire earned a good grade, what is the probability that she studied?

### Probability of Claire earning a good grade is .### Probability that Claire studied given she earned a good grade is .# Calculation Details:### Diagram: ### Calculate Overall Probability of Good Grade:1. Probability Claire works and earns a good grade: \( P(\text{Good Grade} | \text{Work}) = 0.25 \times 0.30 = 0.075 \)2. Probability Claire does not work and earns a good grade: \( P(\text{Good Grade} | \text{No Work}) = 0.75 \times 0.80 = 0.60 \)3. Total Probability \( P(\text{Good Grade}) \): ### Calculate Conditional Probability (Bayes' Theorem): 1. \( P(\text{Good Grade} | \text{Studied}) = 0.80 \)2. \( P(\text{Studied}) = 0.75 \)3. Therefore,