Probability Question for NY State Teaching Exam

Question

Question: Two-fifths of the lawyers at a firm have donated blood in the past year, and one-quarter of them have also played golf in the last month. What percent of the firm’s lawyers have donated blood and played golf?

 

My Work: P(donated) + P(Golf) = Probability firm employees donated blood and played golf.  (2/5) + (1/4) = 8/20 + 5/20 = 13/20= 0.65 = 65%

 

That answer is incorrect but I don't understand why?? The solution set is saying we must multiply both P(donated) and P (Golf) to get the correct answer. But why don't we add?

 

The book gives the correct answer as 10% which is (2/5) x (1/4).

 

Thank you in advance for your explanation.

Answer 1

Poorly worded question. 1/4 of the 2/5 ALSO played golf, not an additional 1/4, so...

 

(1/4)(2/5) = 2/20 = 1/10 = 10%