What is the percentage?

Question

From all the population interviewed 36% respondents had a car at home, 19% had a motorcycle and 4% had both.

I need to find the percentage of respondents having a vehicle either motorcycle or car or both.

Could you please give some hints how to solve this problem ? Thank you

score 2 · Accepted Answer · answered Mar 29 '15 at 12:21

2

$$P(A\cup B) = P(A) + P(B) - P(A\cap B)$$

answered Mar 29 '15 at 12:21

AlexR

1

P(A or B) = 0.36+0.19-0.04=0.51(51%) Right ? – KostasSt7 Mar 29 '15 at 13:15
Yep. That's right. – AlexR Mar 29 '15 at 13:16
I had a thought about that and it does not make sence, I need to get percentage for A or B or both. O got only for a or B – KostasSt7 Mar 29 '15 at 13:20
@KostasSt7 Carefully read the linked wikipedia article. The problem is that $P(A)$ also includes those $4%$ for wich $A$ and $B$ hold at the same time. You want $P(A\cup B) = P(A\setminus B) + P(B\setminus A) + P(A\cap B)$ where $A\setminus B$ denotes set difference ($A$ but not $B$). – AlexR Mar 29 '15 at 13:22
Got it. Thank you very much :) – KostasSt7 Mar 29 '15 at 13:23
@KostasSt7 After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark ✓ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers? – AlexR Mar 29 '15 at 13:25

1 Answers1