Bayes Theorem: Finding a Percentage

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Suppose 50% of people in a particular population have asthma. Of the people with asthma, suppose 75% have heartburn. Whereas, 50% of people without asthma actually have heartburn. What percent of people who have heartburn have asthma?

This is what I have tried

P(asthma) = P(A) = 50%

P(heartburn | asthma) = P(H|A) = 75%

P(heartburn | asthma') = P(H|A') = 50%

I want P(asthma | heartburn) = P(A|H)

$P(A|H) = \frac{P(H|A)*P(A)}{P(H|A)*P(A)+P(H|A')*P(A')} = \frac{(0.75)*(0.5)}{(0.75)*(0.50)+(0.5)*(1-0.5)} = 0.60$

But my solution is incorrect.