Question

1.2 In a group of 60 students, 20 study history, 24 study French and 8 study both history and French .Are the
events ‘a student studies History’ and ‘a student studies French ‘independent?

Answer 1

Two events are independent if the occurrence of one of them does not affect the probability of the occurrence of the other. Now, the probability that a randomly selected student studies French is equal to 24/60 = 2/5. If it is known that the selected student studies history, then the probability that he studies French becomes 8/20 = 2/5. The two obtained probabilities are equal. Hence, the events are independent.

Answer: They are independent.