1) A fair coin is flipped 17 times, and we are interested in the number of heads.

1. What is the probability that the fourth head occurs on the eleventh flip?
2. What is the probability that at least 6 heads will be flipped?
3. What is the probability that the first head occurs on the third flip?
4. What is the probability that less than 10 headswill be flipped?

2)Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average of 4 calls coming per minute.

1. What is the probability that up to a minute will elapse by the time 2 calls have come to the switchboard using the Gamma distribution?
2. What is the probability that less than 30 seconds will elapse between successive calls coming to the switchboard?
3. What is the probability of having at least 3 calls arrive to the switchboard in one minute?
4. What is the probability of having at most 9 calls arrive to the switchboard in three minutes?

3) The proportion of red M&M's in a milk chocolate packet is approximately 20%.Suppose a jumbo package of M&M's typically contains 100 M&M's. What does Chebyshev's theorem tell us about the probability of getting between 14and 26red M&M's?

4) A company ships 5000 cell phones. They are expected to last an average of 10,000 hours before needing repair; with a standard deviation of 500 hours. Assume the survival times of the phones are normally distributed. If a phone is randomly selected to be tracked for repairs find the probability of cell phonesthat need repair.