Statistics and Probability Answers

(5.1.19) The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.
Number of
Girls x P(x)
0 0.005
1 0.003
2 0.115
3 0.234
4 0.246
5 0.234
6 0.115
7 0.023
8 0.005
Find the probability of getting exactly 6 girls in 8 births

(5.1.20) The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.
Number of
Girls x ​P(x)
0 0.005
1 0.006
2 0.114
3 0.204
4 0.342
5 0.204
6 0.114
7 0.006
8 0.005
Find the probability of getting exactly 1 girl in 8 births.

1. The probability of telesales representative making a sale on a customer call is 0.15. Find the probability that
(a) no sales are made in 10 calls, (2 marks) (b) more than 1 sales are made in 20 calls. (3 marks)
Representatives are required to achieve a mean of at least 5 sales each day.
(c) Find the least number of calls each day a representative should make to achieve this requirement. (1 mark) (d) Calculate the least number of calls that need to be made by a representative for the probability of at least 1 sale to exceed 0.95. (3 marks)

Ninety percent of flights depart on time. Eighty percent of flights arrive on time.
Seventy-five percent of flights depart on time and arrive on time. What is the
probability that
a. A flight will arrive on time if it departed on time.
b. A flight will arrive on time if it didn't depart on time.
c. Are the events departing on time and arriving on time independent?

A Ph.D. graduate has applied for a job with two universities: A and B. The graduate
feels that she has a 60% chance of receiving an offer from university A and a 50%
chance of receiving an offer from university B. If she receives an offer from
university B, she believes that she has an 80% chance of receiving an offer from
university A.
a. What is the probability that both universities will make her an offer?
b. What is the probability that at least one university will make her an offer?
c. If she receives an offer from university B, what is the probability that she will
not receive an offer from university A?

What is the probability that a female student will be selected at random from a class
of seven males and three female students, in each of the next two class meetings?

City council consists of nine men and six women. Three representatives are chosen
at random to form a committee. What is the probability that:
a. Two women and a man are chosen?
b. Two women are chosen if Mr. Jim must be on the committee?

In a shipment of 10 electronic components, 2 are defective. Suppose that 5
components are selected at random for inspection. What is the probability that:
a. No defective components are included among the 5 selected?
b. Exactly one defective component being included?

There are 10 students in a class: 6 boys and 4 girls. If the teacher picks a group of
3 at random, what is the probability that everyone in the group is a girl?

A president and a treasurer are to be chosen from a student club consisting of 100
people. How many different choices of officers are possible if
a. Julian and Anton will serve together or not at all?
b. There are no restrictions?
c. Julian will serve only if she is president?
d. Sara and Silvia will not serve together?
e. Note that there are no repeated names in this student club.