Probability Question......

Question

I have this probability question that is driving me bonkers.....

The probability that a high school senior owns a laptop is 0.6. The probability that a high school senior owns a car is 0.2. The probability that a high school senior owns both a laptop and a car is 0.3. What is the probability that a high school senior owns a laptop but not a car?

So my approach was this...

P(owning a laptop) = 0.6 + P(NOT owning a car) = 1-0.2 = 0.8, so 0.6 + 0.8 = 1.4

P(owning neither a laptop nor car) = 1-0.3 = 0.7 so

1.4- 0.7 = 0.7 (probability of owning a laptop but not a car) = 0.7

BUT, that is wrong according to the answer key, apparently it is 0.3.....what am I doing wrong?????

Answer 1

L = event of owning a laptop

C = event of owning a car

P(L) = 0.6

P(C) = 0.2

P(L & C) = 0.3

P(L & !C) = P(L) - P(L & C) = 0.6 - 0.3 = 0.3