The table below shows data from a survey in which customers were asked about their level of satisfaction with the customer service. The customers are split by gender. If a customer is satisfied, find the probability that they are a woman. Round your answer to two decimal places.
In the two-way table, we see that the customers are split by gender: men and women. There were three different responses in the survey. The customers were satisfied, not satisfied, or neutral. We are asked to find the probability that the customer is a woman if they are satisfied.
This is an example of conditional probability, written the probability of 𝐴 given 𝐵. We want to calculate the probability that the customer was a woman given that they were satisfied. We are therefore only interested in the first column: the 27 men and 20 women. This is a total of 47 customers, 20 of whom are women.
As the probability of an event can be written as the number of successful outcomes over the total number of possible outcomes, we have 20 over 47. Typing this into our calculator gives us 0.4255 and so on. We want to round our answer to two decimal places. So the probability that if a customer is satisfied they are a woman is 0.43 to two decimal places.