Exercise 13 Page 773

We have a spinner that is divided into six equal parts, numbered from 1 to 6. We want to find the theoretical probability of the spinner landing on a number which is not less than 3.

Recall that when calculating a probability, we compare the number of favorable outcomes to the number of possible outcomes. P(Event)= Favorable Outcomes/Possible OutcomesNote that the spinner landing on a number not less than 3 is the complement of the spinner landing on a number less than 3. The sum of the probability of an event and the probability of its complement is 1. P(Event)+P(Not event)=1 Let's start by finding the probability of the spinner landing on a number less than 3. 1, 2, 3, 4, 5, 6 The number of favorable outcomes is 2, and the number of possible outcomes is the total number of sections, which is 6. P(Less than3)= Number of parts less than3/Number of parts ⇓ P(Less than3)=2/6 The theoretical probability of the spinner landing on a number less than 3 is 26. Let's now find the probability of its complement.

P(Less than3)+P(Not less than 3)=1

Substitute

P(Less than3)= 2/6

2/6+P(Not less than3)=1

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Solve for P(Not less than3)

SubEqn

LHS-2/6=RHS-2/6

P(Not less than3)=1-2/6

OneToFrac

Rewrite 1 as 6/6

P(Not green)=6/6-2/6

SubFrac

Subtract fractions

P(Not less than3)=4/6

ReduceFrac

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

P(Not less than3)=2/3

We found that the probability of the spinner landing on a number less than 3 is 23.