1 Use Bayes theorem to calculate probabilities Suppose that

1. Use Bayes? theorem to calculate probabilities. Suppose that on the last day of class we have a Pizza party, and 30 students show up. The soft drink company Coca-Cola has determined the probabilities of students ordering a Classic for a drink for various group by age and gender (See Table). (a) Find the probability that a student selected at random orders a Classic. (b) Find the probability that a student that ordered a Classic is a female and under 20?

Solution

a.
Expected number of students that order classic
= 10*0.2 + 15*0.3 + 5*0.1
= 7

total number of students = 10+15+5 = 30

required probability = 7/30

b.
number of students that order classic = 7
number of females under 20 that order classic = 10*0.2 = 2

required probability = 2/7