Exercise 5 Page 902

A camper points a compass in a random direction. We are asked to find the probability that the camper is heading in the N to NE direction. We will use geometric probability. The probability that the camper is heading in the N to NE direction is the same as the ratio of the arc measure of the sector that corresponds to this direction to 360.

As we can see from the given diagram, the arc measure of the sector of the compass that corresponds to this direction is 45^(∘). Let's call the probability of the camper heading in the N to NE direction P(A).

P(A) = 45/360

ReduceFrac

a/b=.a /45./.b /45.

P(A) = 1/8

WriteDec

Write as a decimal

P(A) = 0.125

WritePercent

Convert to percent

P(A) = 12.5 %

The probability that the camper is heading in the N to NE direction is 18, which can be written as a decimal as 0.125, or 12.5 %.