Exercise 10 Page 697

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!

P(AorB)=P(A)+P(B)-P(AandB)

SubstituteValues

Substitute values

P(AorB)=48/162+78/162-14/162

▼

Evaluate right-hand side

AddSubFrac

Add and subtract fractions

P(AorB)=112/162

ReduceFrac

a/b=.a /2./.b /2.

P(AorB)=56/81

CalcQuot

Calculate quotient

P(AorB)=0.691358...

RoundDec

Round to 2 decimal place(s)

P(AorB)≈ 0.69

The probability that the interviewed student won an award for English or mathematics is 5681, or about 0.69.