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Question:

The probabilities of two students A and B coming to the school in time are 3/7 and 5/7 respectively. Assuming that the events 'A coming in time' and 'B coming in time' are independent. Find the probability of only one of them coming to the school in time. Write at least one advantage of coming to school in time.

Solution:

Given:
P(A)=probability of A coming in time = 3/7
P(B)=Probability of B coming in time = 5/7

Probability of only one of them coming to the school in time = P(A∩¬B) + P(¬A∩B)
= P(A)P(¬B) + P(¬A)P(B)
= (3/7)(1 - 5/7) + (1 - 3/7)(5/7)
= (3/7)(2/7) + (4/7)(5/7)
= 6/49 + 20/49
= 26/49

Advantage of coming to school in time: Not missing the morning prayers and/or missing any topic in the first period of class.