If P(color) = 0.53, P(haircut) = 0.40, and P(both) = 0.17, what is P(color and not haircut)?

If P(color) = 0.53, P(haircut) = 0.40, and P(both) = 0.17, what is P(color and not haircut)?

• A. 0.36
• B. 0.53
• C. 0.17
• D. 0.19

Answer: (A)

To find color and not haircut, focus on the part of the color group that doesn’t include a haircut. The probability of color and haircut together is 0.17, and the total probability of color is 0.53. So the portion that is color without a haircut is 0.53 minus 0.17, which equals 0.36. This also checks out since color equals color with a haircut plus color without a haircut: 0.17 + 0.36 = 0.53.

To find color and not haircut, focus on the part of the color group that doesn’t include a haircut. The probability of color and haircut together is 0.17, and the total probability of color is 0.53. So the portion that is color without a haircut is 0.53 minus 0.17, which equals 0.36. This also checks out since color equals color with a haircut plus color without a haircut: 0.17 + 0.36 = 0.53.