Question

A fair spinner has 9 equal sections: 3 red, 2 blue and 4 green.

It is spun twice.

What is the probability of not getting two consecutive blues?

Answer 1

The probability of not getting two consecutive blues is 1 minus the probability of getting two consecutive blues. Since the spinner is fair, the probability of getting a blue on any one spin is $\frac 2 9$ . Since consecutive spins are independent, the probability of getting two consecutive blues is $(\frac 2 9 )^2$ .

Therefore the probability of not getting two consecutive blues is

$1-(\frac 2 9)^2=1-\frac {4} {81}=\frac {77} {81}\approx 95$ %