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Q #16
:

In how many ways can a leap year have exactly one more Monday than the number of Tuesdays?

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Leap year has 52 weeks + 1 day If the first week of year start with Monday then the year will end on Monday, hence, there will be 52 Tuesdays and 53 Mondays


Q #17
:

It is know that Tom and Dick tell the truth only a third of the time (the probability that, each islying is 2/3, every time). Tom makes a statement, and Dick tells us that Tom was speaking the truth. What is the probability that Tom was actually telling the truth?

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              (1/3 *1/3)

--------------------------------- =  1/5

{(1/3 * 1/3) + (2/3 * 2/3)}


Q #18
:

In a race between A and B, the probability of A not losing is 4/5 and that of B not losing is 2/5. What is the probability of a dead heat?

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Prob of A not losing = Prob of A win + Prob of dead heat

similarly for B. So 4/5 + 2/5 = 1 + prob of dead heat. As P(A win) + P(B win) + P(DH) = 1.


Q #19
:

What is the probability that a 5 digit number made from digits 1, 2, 3, 4, 5 and 6 without repetition, is divisible by both 5 and 6, will be

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Divisible by 30. Not possible.

Q #20
:

If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

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