Question

1.A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.08. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 18-year period. Hint: Use the binomial distribution with n = 18 and p = 0.08.

2. According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)

Compute the probability that exactly three of the six M&M’s are green.

Compute the probability that three or four of the six M&M’s are green.

Compute the probability that at most three of the six M&M’s are green.

Compute the probability that at least three of the six M&M’s are green.

3. A small regional carrier accepted 14 reservations for a particular flight with 11 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 43% chance, independently of each other.

Find the probability that overbooking occurs.

Find the probability that the flight has empty seats.

Answer 1