Probability Question

Question

In a group of 50 boys, 18 own a laptop, 20 own a desktop, and of these 6 own both. What is the probability that a boy picked from this group at random owns either a laptop or a desktop computer, but not both.

I answered 13 out of 25 but was told I am wrong. I was told the right answer is 16 out of 25 but I disagree, and they could not explain why 16 was right. Can anyone illuminate this answer for me? Thanks in advance,

Cole

Answer 1

This is very simple, using a Venn diagram.

Draw two circles, L and D, which partially overlap.

The stated values give you a count of 6 in the L∩D region; the number 12 goes into the L-only region and the number 14 goes into the D-only region.

 

Thus the total who have only one of these devices is 12+14 = 26. 

Therefore P(L or D but not both) = 26/50 = 13/25.

 

 

STAND YOUR GROUND--YOU'RE RIGHT.