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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Simulations

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Exercise 27 Page 914

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.

9/14 or about 64.3 %

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 QT is chosen at random, and want to find the probability that the point X lies on QS.

The probability that the point X is on QS is the ratio of the length of QS to the length of QT. P(X is onQS)=QS/QT Looking at the given number line, we can see that QS= 9 and QT= 14.

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

P(X is onQS)=QS/QT

QS= 9, QT= 14

P(X is onQS)=9/14

▼

Convert to percent

Use a calculator

P(X is onQS)=0.642857...

Round to 3 decimal place(s)

P(X is onQS)≈0.643

Convert to percent

P(X is onQS)≈ 64.3 %

The probability that the point X lies on QS is equal to 914 or about 64.3 %.

Subchapter links

Exercises p.911-914