Monday, June 28, 2010

Monday Probability 25: Pairs

A row has a+b chairs. A group has 'a' girls and 'b' boys who sit on the chairs randomly. What is the expected number of pairs (a girl and a boy sitting next to each other)?

Monday, June 21, 2010

Monday Probability 24: Around the Circle

There are m+1 nodes on a circle numbered 0 to m. You are initially at 0 and with equal probability can jump to one of your neighboring nodes. Find the probability that the i-th node is the last node visited, i.e. what is the probability that when node i is eventually visited for the first time, you have visited every other node at least once before that.  

Sunday, June 13, 2010

Monday Probability 23: Three Heads

How many flips on an average will produce three heads in a row?

Answer: 14

Monday, June 7, 2010

Monday Probability 22: Coupons

There are N distinct types of coupons in cereal boxes and each type is equally likely to be in any box. If a child collects n coupons, what is the expected number of distinct coupons types he has?

Monday, May 31, 2010

Monday Probability 21: Boys and Girls

A company is holding a dinner for working mothers with at least one son. Ms. Jackson, a mother with two children, is invited. What is the probability that both children are boys?

Answer: 1/3

Monday, May 24, 2010

Monday Probability 20: Cars on Road

The probability of observing at least one car on a highway during any 20-min time interval is 609/625. What is the probability of observing at least one car during any 5-min interval? Assume uniformity.

Sunday, May 16, 2010

Monday Probability 19: Increasing Dice

We throw 3 dice one by one. What is the probability that we obtain 3 points in strictly increasing order?

Answer: 5/54

Old Problems

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