probability and statistics

Question

Suppose that in a certain population 50% are right-handed, 45% are left-handed and 5% are
ambidextrous. 50% of the right-handed, 80% of the left-handed and 30% of the ambidextrous
can play a musical instrument. If a person chosen at random can play a musical instrument,
what is the probability that the person is ambidextrous?

Answer 1

.05(.3)/(.05(.3)+ .8(.45)+.5(.5))

= .15/(.15+ .36+.25)

= 15/76

= about 20%