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A special promotion for its 20-ounce bottle of soda, a soft drink company printed a
message on the inside of each cap. Some of the caps said, "Please try again," while
others said, "You're a winner!" The company advertised the promotion with the
slogan "] in 6 wins a prize.
Suppose the company is telling the truth and that every 20-ounce bottle of soda it
fills has a 1-in-6 chance of being a winner. Seven friends each buy one 20-ounce
bottle of the soda at a local convenience store. Let X = the number who win a prize.

Respuesta :

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Using the principle of binomial probability, the probability that more than 3 friends win a prize is

Recall :

  • P(x = x) = nCx * p^x * q^(n-x)

Given the Parameters :

  • Probability of success, p = 1/6
  • q = 1 - p = 5/6
  • Number of trials, n = 7
  • x≥3

Hence,

P(x ≥ 3) = p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) + p(x = 7)

P(x ≥ 3) = 0.0781 + 0.0156 + 0.0019 + 0.0001 + 0.000003

P(x ≥ 3) = 0.095703

Therefore, the probability that more than 3 friends win a prize is 0.0957

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