1 A park contains three species of squirrels gray red and fo

1. A park contains three species of squirrels: gray, red, and fox squirrels. If there are 120 gray squirrels, 50 red squirrels, and 30 fox squirrels.

a. What is the probability that the first squirrel you see in the park is a fox squirrel?

b. What is the probability that the first two squirrels you see are gray squirrels?

c. If you see three squirrels, what is the probability that the first one is red, the second is gray, and the third is a fox squirrel?

d. If you see three squirrels, what is the probability that one is red, another is gray, and another is a fox squirrel (in any order)?

2. Suppose there are 42 deer in the woods next to campus. Seven of them are tagged and released. One month later, six deer are captured.

a. What is the probability that none of the deer have tags, assuming that no deer have entered or left the woods?

b. Suppose the woods have a very large population of voles, one-sixth of which are of a smaller species than the rest. What is the probability that, in a random sample of six voles, none of the voles are small?

c. Why are the answers to a. and b. different?

3. A traffic light at an intersection allows traffic to flow along a north-south street for 20 seconds before showing a red light for 40 seconds. What is the probability that you will see a red light on five consecutive approaches to the intersection before catching a green light?

4. Fishing regulations in Michigan require that fish must be released if they are below a minimum size or above a maximum size. Suppose 60% of the fish in a lake are within the legal limits.

a. If you catch five fish, how many of them can you expect to keep?

b. What is the probability that your actual catch will match your expectation?

5. On average, 2.6 people die per day in motor vehicle accidents in the state of Michigan. What is the probability that no one died yesterday in an accident?

Solution

Question answer 1 0.15 2 120(119)/200(199) 3 120(50)(30)/200C3 4 120(50)(30)/200C3*3