Recall the formula for the probability of compound events. Find the probabilities from the formula, substitute them into the formula and isolate P(AandB).
19/200, or 0.095
Practice makes perfect
From the previous example we know that there are 200 students in the senior class, and 51 of them are on the honor roll. We are told that 32 seniors are in the band and 64 seniors are in the band or on the honor roll. We want to find the probability that a randomly selected senior is both in the band and on the honor roll. Start with recalling the formula for the probability of compound events.
P(AorB)=P(A)+P(B)-P(AandB)
In our case event A will represent being in the band and event B will represent being on the honor roll. Since we know that 64 students are in the band or on the honor roll we can calculate P(A or B). To do so we will divide the number of seniors who are in the band or on the honor roll, 64, by the total number number of seniors, 200.
P(AorB)=Band or honor roll/Total number of seniors
Band or honor roll= 64, Total number of seniors= 200
P(AorB)=64/200
Now we will repeat the same procedure for the probability of event A and the probability of event B. We know that 32 seniors are in the band and 51 seniors are on the honor roll. To calculate probabilities of events A and B we need to divide those numbers by the total number of the students, 200.
Probability
P(A)=Number of seniors in the band/Total number of seniors
P(B)=Number of seniors on the honor roll/Total number of seniors
P(A)=32/200
P(B)=51/200
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!
