Show work for everything, plus an explanation, if you could you.

1. is it possible to use the formula p(a and b) = p (a) x p (b|a)when events a and b are independent? explain your reasoning.

2. according to a survey, about 58% of families sit down for a family dinner at least four times per week. you ask 5 randomly chosen families whether they have a family dinner at least four times per week.
a)draw a histogram of the binomial distribution for the survey.
b)what’s the most likely outcome of the survey?
c)what’s the probability that at least 3 families have a family dinner four times per week?

3. the surface area of the earth is about 196.9 million square miles. the land area is about 57.5 million square miles and the rest water. what’s the probability that it will hit the water?

4. three volunteers are chosen at random from a group of 12 to .
a)what’s the probability that you, your friend and your brother is chosen?
b)what’s the probability that you are the cook, your brother the lifeguard, and your friend the counselor? (the first person chosen will be counselor, second will be lifeguard, and third will be the cook.)