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November 5th, 2017, 02:19 PM   #1
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Question Urgent help for upcoming exam

Please help me solving these questions.

1. Assume that the probability of being born on a given day of the year is the same for each of the 365 days. Make a similar assumption for the 12 months. Find the probability that
(a) 2 people met at random on the street have the same birthday,
(b) a person met at random on the street has the same birthday as you,
(c) 3 people met at random on the street were born in 3 different months.

2. In a group of 20 people there are three brothers. The group is separated at random into two groups of 10. What is the probability that the brothers are in the same group? What about if the brothers are four?

3. We throw twice a fair die with 20 (equal) faces labeled 1 to 20. What is the probability that the difference between the higher and the lower outcomes is 2?

4. Four women and four men will seat at a round table for dinner. Each seat is assigned at random to any of the 8 people. What is the probability that each woman will seat between two men? And the probability that all men will seat in consecutive places?

Last edited by skipjack; November 13th, 2017 at 09:25 AM.
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November 13th, 2017, 09:22 AM   #2
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Moved to Probability & Statistics.

(3) For the difference between the higher and the lower outcomes to be 2, the first outcome can be from 1 to 18, the second outcome being two greater, or the first outcome can be from 3 to 20, with the second outcome being two less. Hence the required probability is (18 + 18)/20² = 9/100.
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