To find the probability that the first two randomly selected shoppers bought beauty supplies and the third bought pet supplies, calculate the product of individual probabilities without replacement. After multiplying the probabilities and rounding to three decimal places, the final probability is 0.004.
Step-by-step explanation:
The subject in this question is Mathematics, specifically probability. A survey has been conducted to find out what types of purchases people make online. We need to calculate the probability that the first two shoppers purchased beauty supplies, and the third shopper purchased pet supplies.
The number of shoppers who purchased beauty supplies is the total number of shoppers minus the number who bought food, pet supplies, and toys:
Shoppers who bought food: 23
Shoppers who bought pet supplies: 25
Shoppers who bought toys: 11
So, the number of shoppers who bought beauty supplies = 85 - (23 + 25 + 11) = 26.
The probability of selecting a shopper who bought beauty supplies is therefore (26/85) for the first shopper and (25/84) for the second shopper, since one shopper has already been selected and is not replaced. The probability for selecting a shopper who bought pet supplies as the third one is (25/83), because two shoppers are already selected without replacement.
The combined probability for all three events to happen in sequence is the product of their individual probabilities:
P(first two beauty, third pet) = (26/85) × (25/84) × (25/83)
Calculating this gives:
P(first two beauty, third pet) = 0.0434782608695652 × 0.297619047619048 × 0.301204819277108 = 0.00389863547758285
Rounded to three decimal places, the probability is 0.004.