Exercise 111 Page 522

Consider the Multiplication Rule of Probability.

36 %

Practice makes perfect

From the exercise, we know that the probability of the spinner landing on green twice is 16 %. P(green, green)=0.16 The probability of two events, A and B to occur, is the product of the individual probabilities. Since the same wheel is spun twice, we can write the following equation. P(green) * P(green)=0.16 Let's solve this equation for P(green).

P(green) * P(green)=0.16

ProdToPowTwoFac

a* a=a^2

(P(green))^2=0.16

SqrtEqn

sqrt(LHS)=sqrt(RHS)

P(green)=± sqrt(0.16)

P(green) > 0

P(green)=sqrt(0.16)

UseCalc

Use a calculator

P(green)=0.4

The probability of spinning green on one spin is 40 %. Since the only other color is purple, the probability of the spinner landing on purple must therefore be the complement of this, 60 %. With this, we can calculate the probability of spinning purple twice. P(purple, purple)=0.6* 0.6=0.36 The probability of the spinner landing on purple twice is 36 %.