The probability that a student passes mathematics class is 0.85, the probability that he passes history class is 0.70, and the probability that he passes mathematics and history is 0.50. Are the two events independent of each other?

No

Step-by-step explanation:

To determine if two events are independent, we use the multiplication rule which states P (A and B) = P (A) * P (B).

Here P (math) = 0.85 and P (history) = 0.70. The P (math and history) = 0.50. Multiply the probabilities and see if it is the same as 0.50.

0.85*0.70 = 0.595

It is not the same so these are not independent.