Question

A simple random sample of 8 computer programmers revealed the sex of the programmers and the following information about their weekly incomes.

Programmer	Weekly Income	Sex
A	$550	M
B	$654	M
C	$911	F
D	$500	M
E	$727	M
F	$688	F
G	$1000	F
H	$892	M

1. If all the salaries were written on separate pieces of paper, and one was drawn at random, what is the probability that the one that was drawn would be over $700?
2. If a programmer were selected at random to complete a project, what would the probability be that the programmer was male?
3. What is the probability of selecting an income of under $700 per week given that a male was selected?
4. If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that both were female?
5. If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that the first draw would be the salary of a male and the second would be one of a female?

Answer 1

1. Since there are 4 programmers out of 8 whose salaries are above 700$. So, the probability of picking one of them is 0.5.

2. Since 5 programmers out of the 8 are Male, the probability of picking a male is 5/8 = 0.625

3. Among the 5 males, since 3 males earn less than $700, the probability of picking them given it is a male is 3/5 = 0.6.

4. Since, now there will be 16 slips, 8 containing the salary and 8 containing who earned those salaries. We are choosing 2 of them. Now, there are 6 slips which belong to females.

$\text{P(both being females)} = \frac{{6\choose 2}}{{16\choose 2}} = \frac{15}{8\times 15} = \frac{1}{8} = 0.125$