We are told that a company is focus testing a new type of fruit drink. The focus group is 47% male. Of the responses, 40% of males and 54% of females said that they would buy the drink. We want to find the probability that a randomly selected person would buy the fruit drink. Let's starting by naming the events.
A& - Person is a male.
B& - Person would buy the drink.
Note that when event A occurs P(B)=40%=0.4, and when event A does not occur P(B)=54%=0.54. The probability of event B depends on the occurrence of event A, so the events are dependent. Let's now consider the probabilities on a probability tree diagram. Note that the event of a person being a female is a complement of event A, so we will mark it as A.
Since on the tree diagram there are complements of events A and B, we can use the formula for the probability of a complement to calculate their probability.
P(A)& =1- 0.47= 0.53
P(B|A)& =1- 0.4= 0.6
P(B|A)& =1- 0.54= 0.46
Let's add the obtained information to our diagram.
To find the probability that a person would buy the drink, we need to follow the branches of our diagram leading to event B. We have two ways leading to event B. We have to multiply the values on each way, and then add the values from both ways.
