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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

3. Geometric Probability

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Exercise 9 Page 902

In geometric probability, points on a segment or in a region of a plane represent outcomes. The geometric probability of an event is a ratio that involves geometric measures such as length or area.

1/9, 0.11, or about 11 %

Practice makes perfect

We can use geometric models to solve certain types of probability problems. In geometric probability, points on a segment or in a region of a plane represent outcomes. The geometric probability of an event is a ratio that involves geometric measures such as length or area. Consider the given diagram.

We are told that a point on FK is chosen at random, and want to find the probability that the point X lies on FG.

The probability that the point X is on FG is the ratio of the length of FG to the length of FK. P(X is onFG)=FG/FK Looking at the given number line, we can see that FG= 4 and FK= 36.

We can substitute these values in the above formula to find the probability that the point lies on FG.

P(X is onFG)=FG/FK

FG= 4, FK= 36

P(X is onFG)=4/36

a/b=.a /4./.b /4.

P(X is onFG)=1/9

▼

Write as a decimal

Use a calculator

P(X is onFG)=0.1

Round to 2 decimal place(s)

P(X is onFG)≈ 0.11

Convert to percent

P(X is onFG)≈11 %

The probability that the point X lies on FG is equal to 19, which can be also written as 0.11 or about 11 %.

Subchapter links

Exercises p.902-905