Question

As per college records, the probability of a student taking a chemistry course is 0.40, the probability to take an Arabic course is 0.55, and the probability of taking both courses is 0.15. Which of the following is true?

1- "Taking Chemistry" and "Taking Arabic" are independent but not mutually exclusive events.


2- "Taking Chemistry" and "Taking Arabic" are independent and mutually exclusive events.


3- "Taking Chemistry" and "Taking Arabic" are mutually exclusive but not independent events.


4- "Taking Chemistry" and "Taking Arabic" are neither mutually exclusive nor independent events.

Answer 1

The correct option is 3-"Taking Chemistry" and "Taking Arabic" are mutually exclusive but not independent events.

Mutually exclusive events are events that cannot happen at the same time, meaning P(A and B) = 0. In this case, P(Taking Chemistry and Taking Arabic) = 0.15, so the events are not mutually exclusive.

Independent events are events where the occurrence of one event does not affect the occurrence of another event, meaning P(A and B) = P(A) * P(B). In this case, P(Taking Chemistry and Taking Arabic) ≠ P(Taking Chemistry) * P(Taking Arabic) = 0.40 * 0.55 = 0.22, so the events are not independent.