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A coin is Flipped 3 times. What IS the probability that the coin lands heads up once and tails up twice if order does not matter?

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Answer:

The probability that the coin lands heads up once and tails up twice is .375, or 3/8.

Step-by-step explanation:

Check the conditions for a binomial distribution problem:

  • Define success = heads and failure = tails.
  • The number of trials is fixed; n = 3.
  • Each coin flip is independent of the other.
  • Probability p = .5 of getting either heads or tails.

We need to use combinations to determine the probability of getting one success (one head) and two failures (two tails).

The combination would be 3 choose 1:  [tex]p = {3 \choose 1} (.5)^1(.5)^2[/tex].

There is one success and two failures, denoted by the superscripts above the probability p = .5.

Use a calculator to evaluate and we get:

  • [tex](3)(.25)(.5) = .375[/tex]

The probability that the coin lands heads up once and tails up twice is .375, or 3/8.

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