This is question 11 from the old midterm in the Documentation folder
11. The ship has two entertainers, who aren't very good. One is a lady opera singer, and the other a dance instructor. They hate each other and act quite independently. The opera singer has a bad temper and the probability of her being in a good enough temper to sing is 0.4. The dance instructor is frequently drunk and unable to stand, let alone teach dancing. The probability of him being drunk is 0.6. Draw a probability tree and find:]
a. (6) That both of them are able to perform on any one night?
b. (6) The probability that one and only one of them can perform on any one night?
Solution: notice the word 'independently'. This means that you can multiply the probabilities. They are independent, so P(A|B) = P(A).
Draw a probability tree (see the Youtube, link at top of page).
Answer to 'a' is Probability singer sings * Probability dance instructor not drunk = 0.4 * 0.4 = 0.16
For 'b' the event contains two sample points---singer sings * dancer drunk + singer doesn't sign * dancer not drunk
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