Class records at Rockwood College indicate that a student selected at random has probability 0.78 of passing French 101. For the student who passes French 101, the probability is 0.81 that he or she will pass French 102. What is the probability that a student selected at random will pass both French 101 and French 102? (Round your answer to three decimal places.)

63.2% probability that a student selected at random will pass both French 101 and French 102

Step-by-step explanation:

We have these following probabilities:

0.78 = 78% probability that a student passes French 101.

0.81 = 81% probability that a student passes French 102.

What is the probability that a student selected at random will pass both French 101 and French 102?

These probabilities are independent, since for the student to take French 102, he has to pass French 101. So we just multiply these probability to find the probability of both events happening.

0.78*0.81 = 0.632

63.2% probability that a student selected at random will pass both French 101 and French 102