# Monday Probability

Come every Monday, something will puzzle you. Come every Monday, something will challenge you. Come every Monday, something will sound interesting. Come every Monday, the beauty of the random world will engage you! So, come every Monday.

## 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

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

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

Answer: 5/54

Subscribe to:
Posts (Atom)