Question

A fair spinner has 11 equal sections: 3 red, 4 blue and 4 green. It is spun twice. What is the probability of getting the same colour twice?

Answer 1

The probability of getting the same colour twice is approximately 34%.

Explanation:

The probability of getting each color is:

• P(x=red) = 3/11
• P(x=blue) = 4/11
• P(x=green) = 4/11

Then, we can calculate the probability of getting the color red twice as:

`P(x_1=R;x_2=R)=P(x=R)^2=(3/11)^2=9/121`

We have to repeat this for the color blue and green:

`P(x_1=B;x_2=B)=P(x=B)^2=(4/11)^2=16/121\\\\P(x_1=G;x_2=G)=P(x=G)^2=(4/11)^2=16/121`

Then, the probability of getting the same color twice in two spins can be calculated as:

`P=P(x_1=R;x_2=R)+P(x_1=B;x_2=B)+P(x_1=G;x_2=G)=\\\\P=9/121+16/121+16/121\\\\P=41/121\approx0.34`