Conditional Probability canvasser Questions

Question

I have to asnswer the following question :

A canvasser is told that 60% of the people in her ward vote for her party. She is also told that 50% of the supporters of her party own bicycles while the overall figure for cycle ownership for the rest is just 25%. What proportion of people in her ward own bicycles?

I think the answer is 55% however I am not sure on what method or formula to use to show my working. Thank you in advance.

Answer 1

$60$% of all people are supporters, and $50$% or half of them own bicycles, which means $30$% of all people are supporters AND own bicycles.

$40$% of all people are non-supporters, and $25$% or a quarter of them own bicycles, which means there is a $10$% of all people are non-supporters AND own bicycles.

You can calculate the result by yourself, and it is not $55$%.

Answer 2

Suppose there are $n$ people total in her ward.

$0.60n$ voted for her party.

$0.50(0.60n)=0.30n$ amongst her supporters own bicycles.

$(1.00-0.60)n=0.40n$ did not vote for her party.

$0.25(0.40n)=0.10n$ amongst her non-supporters own bicycles.

Total $(0.30+0.10)n=0.40n$ own bicycles in her wards

Therefore, $40\%$ of the people own bicycles.

Answer 3

$50\%$ of the $60\%$ who voted for her party, and $25\%$ of those not in that $60\%$, own bicyles. So clearly the percentace of bicyle owners among the total population is: $$(0.50\times 0.60)+(0.25\times(1-0.60)) = \underline\qquad$$