Question Video: Calculating a Conditional Probability from a Two-Way Table | Nagwa Question Video: Calculating a Conditional Probability from a Two-Way Table | Nagwa

Question Video: Calculating a Conditional Probability from a Two-Way Table Mathematics • Third Year of Secondary School

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The owner of a store records customer buying habits on sales of two of the store’s popular products: soda and candy. Given that a customer is not buying candy, find the probability that they are not buying soda. Give your answer to two decimal places.

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Video Transcript

The owner of a store records customer buying habits on sales of two of the store’s popular products: soda and candy. Given that a customer is not buying candy, find the probability that they are not buying soda. Give your answer to two decimal places.

We’ve been given the data on whether customers are buying soda, candy, both, or neither in a two-way table. From the table, we can see that, for example, there were 110 customers who bought both candy and soda. And there were 35 customers who bought soda but did not buy candy.

In questions like these, we’ll usually need to know the row and column totals and the overall total. So we can extend the table to include these values. Summing across the rows, the total number of customers who bought soda, regardless of whether or not they also bought candy, was 145. And the total number of customers who did not buy soda was 48. Summing down the columns, the total number of customers who bought candy, regardless of whether or not they also bought soda, was 150. And the total number of customers who did not buy candy was 43. We can find the total number of customers who visited the store by summing the row totals or by summing the column totals. And we should get the same overall total in both cases. We do; the total number of customers who visited the store was 193.

We’re then asked to find a particular probability. Given that a customer is not buying candy, we need to find the probability that they are not buying soda. Now, what we’re being asked to calculate here is actually a conditional probability. We’ve been given some information about this customer, which is that they are not buying candy. This means that we’re no longer interested in all 193 customers, but just those who didn’t buy candy, the total of which is 43. Of these 43 customers, eight of them did not buy soda. So, if we know the person isn’t buying candy, then the probability that they also aren’t buying soda is eight out of 43.

We’re asked to give this probability to two decimal places though. So we need to convert this fraction to a decimal. It’s 0.1860 continuing, which to two decimal places is 0.19.

Using the two-way table, we’ve found that the probability a customer is not buying soda, given that they are not buying candy, is 0.19 to two decimal places.

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