Amy S.

# Another probability question

a pupil travels to school either by MRT or by bus. Th probability that the pupil will be late for school is 1/12 if he travels by MRT and 1/9 if he travels by bus.

a) if he travels by bus on two consecutive days, find the probability that he will be late for school on one out of the 2 days. Give your answer as a fraction reduced to its simplest form.

b) if he is equally likely to travel by MRT or by bus, calculate the probability that he will not be late for school on any given day

c) what is the probability that he will travel by MRT in two successive days and he will not be late on both days? (Given that he is equally likely to travel by a MRT or by bus)

May I have step by step workings please? I don't understand how to do this question!

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Amy S.

Hi, I got 1/9 for part a, 29/36 for part b and 11/12 for part c. But I feel that some of the answers are wrong. Able to advise on how to do? :)
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01/26/18

Kenneth S.

For b) I get 65/72 = 0.902777... which seems reasonable (the two probabilities for lateness being 0.08333 and 0.111... and that's an average 7/72 or 0.097 (this is just a crude check).

I may look at c) when I clear my desks of other business.
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01/26/18

Kenneth S.

Note that I have modified the answer for a).

For c), we'll assume MRT transportation used on two consecutive days. The question asks for probability of not being late on both days. This means, to me, that he could be on time both days, or late on exactly one of the two days.

We should use Binomial Distribution: (late + not.late)2 = (1/12)+ 2(1/12)(11/12) + (11/12)2 is the expansion; first term is probability of on time both days; last term is probability of late both days; middle term is probability of one late, one on time.

Therefore P(not late on 2 consec. days, by MRT) = the sum of the first two terms above; this is 1 - (11/12)2.
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01/26/18

Amy S.

For part c, you mentioned the first term was the probability of on time both days which is (1/12)^2. But isn't 1/12 the probability that the pupil will be late if he travels by MRT?
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01/26/18

Kenneth S.

My (final) ANSWER for a) is NOT 1/81.  Calculate a & b as I noted, then 1-a-b.

c) The binomial expansion is typed (laboriously) is correct. It represents probability of being late (by MRT) both days--you correctly detected a mistake in my typing (I said on time rather than late! With that corrected verbiage, I think the problem is correctly explained.
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01/27/18

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