Two-way
With tables, you have to cover up the areas that are not true (from what was given -
already true) and then figure out the total possible and the event occurrences. In the
examples below, we will use the table below listing employees years of service:
Years
0-4
5-9
10-14
14+
Totals
Males
12
6
17
21
56
Females
8
9
13
14
44
Totals
20
15
30
35
100
1. What is the probability of randomly selecting a female employee?
44 female employees out of 100 total;
P(F) 44/100 = 0.44
2. Given that the employee is male, what is the probability that they have less than 4
years of experience?
Only look at the male row! 12 males in 0-4 out of 56 total; P(0-4|M) = 12/56 = 0.21
3. Given that the employee has between 10 and 14 years of experience, what is the
probability that the employee is female?
Only look at the 10-14 yr column! 13 females out of 30 in 10-14; P(F|10-14) = 13/30 = 0.43
4. Given that the employee has more than 14 years of experience, what is the probability
that the employee is male?
Only look at the 14+ yr column! 21 males out of 35 in 14+; P(M|14+) = 21/35 = 0.60
5. What is the probability of randomly selected an employee with less than 14 years of
experience given that they are female?
Use complement! P(<14|F)=1-P(>14|F)=1-14/44 = 30/44 = 0.68