Hello my name is Amy. I am a student and need help on some probability questions
I really need your help on some problems dealing with probability. If you will show me how to do the following:

1. The table below represents a random sample of the number of deaths per 100 cases for a certain illness over time. If a person infected with this illness is randomly selected from all the infected people, find the probability that the person lives for 3-4 years after their diagnosis.

Years of Diagnosis Number of Deaths
1-2 15
3-4 35
5-6 16
7-8 9
9-10 6
11-12 4
13-14 2
15+ 13

2. An ice chest contains 9 cans of apple juice, 8 cans of grape juice, 7 cans of orange juice, and 5 cans of pineapple juice. Suppose you reach into the container and randomly select 3 cans in succession. What's the probability of selecting no grape juice?

3. Suppose a basketball player is an excellent free throw shooter and makes 90% of his free throws and assuming that free throw shots are independent of one another. The player gets to shoot 4 free throws. What's the probability that he MISSES all four consecutive free throws.

4. The probability that a region prone to hurricanes will be hit by a hurricane in any single year is 1/5. What's the probability of a hurricane at least once in the next 5 years?

5. A company employs 34 workers who interview clients. Sometimes the supervisor, at random, selects work from the workers to check it for illegal activity. Unknown to the supervisor is that 8 of the workers are performing illegal activities. Given the first worker chosen has not been performing illegal activities what is the probability that the second worker chosen has been doing illegal activities.

Amy showed us what she had done.

On prob number 1. I have all deaths total being 100, the people who will survive for 3-4 years as being 65 (compliment of 35) in the table. So is the probability 65/100?

I interpreted this to be asking the probability that a person lives 3 or 4 years or more after the diagnosis. If this is the correct interpretation then you want the complement of dying in the first 1 or 2 years.

On prob 2, I know this is a combination question but it deals with a 0 which I don't know how to do.

The number of ways of choosing 3 cans from 29 is 29 choose 3. If you disregard the 8 cans of grape juice then the number of ways of choosing 3 cans from 21 is 21 choose 3.

On number 3, I have the event is 4 independent misses. So P(E) is .10 to the power of 4 which is .0001 is this the way to do this problem?

Yes.

Num 4. If a region has a 1/5 probability that a hurricane will hit then the odds that it will hit at least one in next five years is 1?

I think, like in problem 3 you should assume that the event of being hit by a hurricanes in any year is independent of whether you are hit in any other year. Find the probability that you don't get hit in any of the next 5 years and then take the complement.

No. 5 This one has so many factors I don't know how to set it up. Can you help me?

This is a conditional probability question. You want to know the probability that the second worker chosen has been doing illegal activities given that the first person chosen has not has been doing illegal activities. So after the first person is chosen there are 33 workers left. 25 of them have not been doing illegal activities and 8 of them have. Thus if you choose one of these workers at random the probability is 8/33 that this worker has been doing illegal activities.

Harley