Consider the following categorical variables: gender and college major. Consider these four hypothetical joint probabilities: P(male AND major in...

Consider the following categorical variables: gender and college major. Consider these four hypothetical joint probabilities:

                        P(male AND major in physical sciences)            = .35

                        P(male AND not major in physical sciences)      = .20

                        P(female AND major in physical sciences)         = .15

                        P(female AND not major in physical sciences)  = .30

a. Construct a probability tree for the events shown. Place the gender variable first in the tree.

b. Find P(male) and P(female).

c. Redraw the probability tree and place the college major variable first in the tree.

d. Find P(major in physical sciences) and P(not major in physical sciences).