Question

1. A poll is given, showing 20% are in favor of a new building project.
If 10 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

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%.)
a.) Compute the probability that exactly two of the six M&M’s are yellow.
b.) Compute the probability that two or three of the six M&M’s are yellow.
c.) Compute the probability that at most two of the six M&M’s are yellow.
d.) Compute the probability that at least two of the six M&M’s are yellow.

3. A small regional carrier accepted 11 reservations for a particular flight with 10 seats. 7 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 40% chance, independently of each other.
a.) Find the probability that overbooking occurs.
b.) Find the probability that the flight has empty seats

4. The Smith family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had:a.) at least 3 girls?
b.) at most 3 girls?

5. 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 0.14.
• 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 3 tornadoes in a 10-year period.

Answer 1

1) Let x be the number of people favor of a new building project.

Binomial problem with n=10, p= 0.20 and x= 4

    binomial formula is

=   

     = 0.0880

2)   Here, x = number of yellow candies

a.) Compute the probability that exactly two of the six M&M’s are yellow.

    P(x=2) = = 0.1762

b.) Compute the probability that two or three of the six M&M’s are yellow.

    P(x=2) + P(x=3)

=

=0.1762 + 0.0415

= 0.2177

c.) Compute the probability that at most two of the six M&M’s are yellow.

    P(x=0) + P(x=1) + P(x=2)

=

=0.3771+0.3993+ 0.1762 = 0.9526

d.) Compute the probability that at least two of the six M&M’s are yellow.

    P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6)

=

= 0.1762+ 0.0415 +0.0055 + 0.0004 + 0

= 0.2236