1. Suppose a family has four children.
   1. What is the sample space?
   2. What is the probability of 4 boys? 4 girls?
   3. What is the probability of 1 girl and three boys? 1 boy and three girls?
   4. What is the probability of 2 boys and 2 girls?
   5. What is the sum of your answers in parts b through d?
2. What is the probability of a family of three children consisting of two boys given that at least one of them is a boy? (Assume the probability of a boy child is the same as a girl child.)
3. A couple has two children. What is the probability that both are girls if the eldest is a girl? (Assume the probability of a boy child is the same as a girl child.)
4. What is the probability of flipping a coin four times and obtaining three heads, given at least two are heads?
5. A chairman and a vice-chairman of a board consisting of 10 men and 5 women are to be chosen. After a chairman is chosen, what is the probability that the vice-chairman is a woman?
6. Two fair dice are rolled. What is the conditional probability that the first one lands on 6 given that the dice land on different numbers?
7. What is the probability that at last one of a pair of fair dice lands on $6$ given that the sum of the dice is $j$, .
8. Three cards are randomly selected, without replacement, from an ordinary deck of 52 playing cards. Compote the conditional probability hat the first card selected is a spade, given that the second and third cards are spades.

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Math 804T
Experimentation, COnjecture, and Reasoning
Fall, 2007

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