Recall the formula for the probability of compound events. Then find the probability of each event by dividing the number of favorable outcomes by the total number of possible outcomes.
56/81, or about 0.69
Practice makes perfect
Of 162 students honored at an academic awards banquet, 48 won awards for mathematics, 78 for English, and 14 students won awards for both mathematics and English. The newspaper a student at random for an interview. We want to find the probability that the interviewed student won an award for English or mathematics. Recall the formula for the probability of compound events.
P(AorB)=P(A)+P(B)-P(AandB)We can mark the event of receiving an award for mathematics as A, and the event of receiving an award for English as B. To calculate the needed probabilities we need to divide the number of favorable outcomes for every event by the total number of possible outcomes, 162. Recall that 48 students won an award for mathematics, 78 for English, and 14 won both.
Event
Favorable Outcomes
Probability
A
B
A and B
48
78
14
48/162
78/162
14/162
Now we can substitute the obtained probabilities into the formula for the probability of compound events, and find the value of P(AorB). Let's do it!
