A total of 191 shoppers at a large suburban mall were asked two questions: 1. Did you see a TV ad for the sale at store M? 2. Did you shop at store M? 89 shoppers indicated they had seen the advertisement; 65 had seen the ad and did not shop at M; 94 shoppers had not shopped at M. One of the shoppers is chosen at random. What is the probability that the person saw the ad and shopped at M? ( 2 dec pl)
Question
A total of 191 shoppers at a large suburban mall were asked two questions:
- Did you see a TV ad for the sale at store M?
- Did you shop at store M?
89 shoppers indicated they had seen the advertisement; 65 had seen the ad and did not shop at M; 94 shoppers had not shopped at M. One of the shoppers is chosen at random. What is the probability that the person saw the ad and shopped at M? ( 2 dec pl)
Solution
Step 1: Identify the total number of shoppers. In this case, it's 191.
Step 2: Identify the number of shoppers who saw the ad and did not shop at M. This is 65.
Step 3: Identify the number of shoppers who saw the ad. This is 89.
Step 4: Subtract the number of shoppers who saw the ad and did not shop at M from the total number of shoppers who saw the ad. This will give you the number of shoppers who saw the ad and shopped at M.
So, 89 (shoppers who saw the ad) - 65 (shoppers who saw the ad and did not shop at M) = 24 (shoppers who saw the ad and shopped at M).
Step 5: To find the probability that a randomly chosen shopper saw the ad and shopped at M, divide the number of shoppers who saw the ad and shopped at M by the total number of shoppers.
So, 24 (shoppers who saw the ad and shopped at M) / 191 (total shoppers) = 0.1256544502617801.
Step 6: To convert this to a percentage with two decimal places, multiply by 100 and round to the nearest hundredth.
So, 0.1256544502617801 * 100 = 12.57%.
Therefore, the probability that a randomly chosen shopper saw the ad and shopped at M is approximately 12.57%.
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