Tree Diagrams and Normal Curves

1. Suppose that a couple will have three children. Letting B denote a boy and G denote a girl:
a) Draw a tree diagram depicting the sample space outcomes for this experiment.
b) List the sample space outcomes that correspond to each of the following events:
1. All three children will have the same gender
2. Exactly two of the three children will be girls
3. Exactly one of the three children will be a girl.
4. None of the three children will be a girl.
c) Assuming that all sample space outcomes are equally likely, find the probability of each of the events given in part (b)

2. John and Jane are married. The probability that John watches a certain television show is 0.4. The probability that Jane watches the show is 0.5. The probability that John watches the show, given that Jane does, is 0.7.
a) Find the probability that both John and Jane watch the show.
b) Find the probability that Jane watches the show, given that John does.
c) Do John and Jane watch the show independently of each other? Justify answer.

3. Suppose that the probability distribution of a random variable x can be described by the forma p(x)=x/15 (x over 15). For each of the values x=1,2,3,4, and 5. For example, then P(x=2)=p(2)=2/15
a) Writhe out the probability distribution of x.
b) Show that the probability distribution of x satisfies the properties of a discrete probability distribution.
c) Calculate the mean of x.
d) Calculate the variance and the standard deviation.

4. Sketch the two specified normal curves on the same set of axes:
A normal curve with Ã?µ=20 and x=3, and a normal curve with Ã?µ=20 and x=6.