Exercise 17 Page 153

Practice makes perfect

a To determine probability, we divide the number of favorable outcomes with the number of possible outcomes.

P=Number of favorable outcomes/Number of possible outcomes From the exercise, we know that the number of possible outcomes is 20 and that the favorable outcomes of picking a girl is 10. With this, we can calculate the probability of the first contestant being a girl.

P=Number of favorable outcomes/Number of possible outcomes

SubstituteValues

Substitute values

P=10/20

ReduceFrac

a/b=.a /10./.b /10.

P=1/2

The probability that a girl is selected is 12 or 50 %

b If the first contestant is a girl, then the number of favorable outcomes and possible outcomes will both be one less.

Girls:& 10-1=9 Contestants:& 20-1=19 Now we can calculate the probability of picking a girl the second time.

P=Number of favorable outcomes/Number of possible outcomes

SubstituteValues

Substitute values

P=9/19

CalcQuot

Calculate quotient

P=0.47368...

RoundDec

Round to 2 decimal place(s)

P≈ 0.47

The probability that a girl is selected a second time is about 47 %

c If two events are independent, the probability of one event does not affect the probability of the other. In this case, if the first contestant picked is a girl, it will affect the number of favorable and possible outcomes when the second contestant is picked. Therefore, the events are dependent.

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