Recall the formula for the probability of compound events. Find the probabilities from the formula, substitute them into the formula, and isolate P(AandB).
16, or about 0.17
Practice makes perfect
The company paid overtime wages or hired temporary help during 9 months of a year. Overtime wages were paid during 7 months, and temporary help was hired during 4 months. We want to find the probability that an auditor examining the accounting records will select the month in which the company both paid overtime and hired help. Recall the formula for the probability of compound events.
P(AorB)=P(A)+P(B)-P(AandB)
In our case event A will represent paying overtime wages and event B will represent hiring temporary help. Since we know that during 9 months the company paid overtime or hired temporary help, we can calculate P(A or B). To do so we will divide the number of months in which company paid overtime or hired help, 9, by the total number number of months in a year, 12.
Now we will repeat the same procedure for the probability of event A and the probability of event B. We know that during 7 months the company paid overtime wages and during 4 months they hired temporary help. To calculate probabilities of events A and B we need to divide those numbers by the total number of months in a year, 12.
Probability
P(A)=Number of months with paying overtime/Total number of months
P(B)=Number of months with temporary help/Total number of months
P(A)=7/12
P(B)=4/12
Note that now we know every value from the formula for the probability of compound events except the value of P(AandB). Therefore, we can substitute the obtained values into this formula and isolate P(AandB). Let's do it!
