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Assist with these HW questions How many outcomes are possible when flipping a coin 3 times and rolling a six-sided die 4 times? In the

Assist with these HW questions

  1. How many outcomes are possible when flipping a coin 3 times and rolling a six-sided die 4 times?
  2. In the Olympics 100-meter final, how many different ways can the 8 finalists finish first, second or third (only the top three positions matter
  3. A convenience store has found that the probability that a soda sold in the store is a Coke is 0.7. The probability that the soda is any other brand is 0.3. The probability that the soda is a diet soda given it is a coke is 0.2. The probability that it is a diet soda given it is any other brand is 0.4. What is the probability that any given soda sold is a diet soda?
  4. Historical data shows that 0.15% of finished products from of a production line is faulty and must be either refurbished or scrapped.You are inspecting a box of 20 units from the latest production batch. What is the probability that you will find one faulty unit? Assume Binomial distribution.
  5. Historical data shows that 0.15% of finished products from of a production line is faulty and must be either refurbished or scrapped. You are inspecting a box of 20 units from the latest production batch. What is the probability that you will find at most 3 faulty units? Assume Binomial distribution.
  6. Historical data shows that 0.15% of finished products from of a production line is faulty and must be either refurbished or scrapped.You are inspecting a box of 20 units from the latest production batch. What is the probability that you will find at least 5 faulty units? Assume Binomial distribution.
  7. Historical data shows that 0.15% of finished products from of a production line is faulty and must be either refurbished or scrapped.You are inspecting a box of 20 units from the latest production batch. What is the expected number of faulty items?
  8. A local bar keeps records of Happy Hour (5:00 P.M. to 6:00 PM), number of customers arriving. On average, 10 customers arriving during the happy hour. Let's assume these arrivals follow the Poisson distribution. On a given day, what is probability of exactly 9 customers will arrive during the Happy Hour?

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