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A restaurant has an electronic system that randomly selects customers when they pay for their meal to receive a coupon for their next visit. Each customer has a 10% probability of being selected to receive a coupon, and one customer being selected or not doesn't affect whether or not another customer will be selected. Suppose that 2 customers pay for their meals, one after the other. What is the probability that NEITHER customer is selected to receive a coupon? Round your answer to two decimal places.

A restaurant has an electronic system that randomly selects customers when they pay for their meal to receive a coupon for their next visit. Each customer has a 10% 10 \% probability of being selected to receive a coupon, and one customer being selected or not doesn't affect whether or not another customer will be selected.\newlineSuppose that 22 customers pay for their meals, one after the other.\newlineWhat is the probability that NEITHER customer is selected to receive a coupon?\newlineRound your answer to two decimal places.

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Q. A restaurant has an electronic system that randomly selects customers when they pay for their meal to receive a coupon for their next visit. Each customer has a 10% 10 \% probability of being selected to receive a coupon, and one customer being selected or not doesn't affect whether or not another customer will be selected.\newlineSuppose that 22 customers pay for their meals, one after the other.\newlineWhat is the probability that NEITHER customer is selected to receive a coupon?\newlineRound your answer to two decimal places.
  1. Understand Probability: Understand the probability of one event not happening.\newlineThe probability of one customer not being selected for a coupon is the complement of the probability of them being selected. Since each customer has a 10%10\% chance of being selected, they have a 90%90\% chance of not being selected.\newlineCalculation: 100%−10%=90%100\% - 10\% = 90\% or 0.900.90 in decimal form.
  2. Calculate Individual Probability: Calculate the probability of both independent events not happening.\newlineSince the selection of one customer does not affect the selection of another, we can multiply the probabilities of each customer not being selected to find the combined probability.\newlineCalculation: 0.900.90 (probability of first customer not being selected) ×\times 0.900.90 (probability of second customer not being selected) =0.81= 0.81.
  3. Calculate Combined Probability: Convert the decimal probability to a percentage and round to two decimal places.\newlineCalculation: 0.81×100%=81%0.81 \times 100\% = 81\%.\newlineRounded to two decimal places, the probability remains 81%81\%.

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