I need the answers for this for study and showing the work here or in Excel to show work.

1.What is the probability of at least one head in two flips of a coin?

2.What is the meaning of mutually exclusive events?

3.The results of a survey of 800 married couples and the number of children they had is shown below.

Number of Children

Probability

0

0.050

1

0.125

2

0.600

3

0.150

4

0.050

5

0.025

If a couple is selected at random, what is the probability that the couple will have

a.Less than 4 children?

b.More than 2 children?

c.Either 2 or 3 children?

4.A government agency has 6,000 employees. The employees were asked whether they preferred a 4-day work week (10 hours per day), a 5-day work week (8 hours per day), or flexible hours. You are given information on the employees' responses broken down by gender.

Male

Female

Total

4 days

300

600

900

5 days

1,200

1,500

2,700

Flexible

300

2,100

2,400

Total

1,800

4,200

6,000

a.What is the probability that a randomly-selected employee is a man and is in favor of a 4-day work week?

b.What is the probability that a randomly-selected employee is female?

c.A randomly-selected employee turns out to be female. Compute the probability that she is in favor of flexible hours.

d.What percentage of employees is in favor of a 5-day work week?

e.Given that a person is in favor of flexible time, what is the probability that the person is female?

f.What percentage of employees is male and in favor of a 5-day work week?