A student attends either a Mathematics class or an Additional mathematics class everyday. The probability of him bringing the wrong textbook is 3/5 if he attends the Mathematics class and 3/10 if he attends the Additional Mathematics class.
(a) If he attends Mathematics class on three consecutive days, find the probability that he will bring the wrong textbook
(i) on all the three days
(ii) on just one of the three days.
(b) If he is equally likely to attend the Mathematics class or the Additional Mathematics class, find the probability that he will bring the correct textbook to class on any given day.
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Answer:
(a)
(i) P(wrong textbook on all three days)
= P(1st day wrong textbook) * P(2nd day wrong textbook) * P(3rd day wrong textbook)
= 3/5 * 3/5 * 3/5
= 27/125
(ii) P(just one of three days wrong textbook)
= P(1st day wrong, 2nd, 3rd day correct) + P(2nd day wrong, 1st, 3rd day correct) + P(3rd day wrong, 1st, 2nd day correct)
= 3/5 * 2/5 * 2/5 + 2/5 * 3/5 * 2/5 + 2/5 * 2/5 * 3/5
= 36/125
(b) P(correct textbook for Mathematics or for Additional Mathematics)
= P(attend Mathematics and bring correct txtbook for Mathematics) + P(attend Additional Mathematics and bring correct txtbook for Additional Mathematics)
= 1/2 * 2/5 + 1/2 * 7/10
= 11/20
