Question

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?

Answer 1

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

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:
`p = {3 \choose 1} (.5)^1(.5)^2`.

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

Use a calculator to evaluate and we get:

• 
  `(3)(.25)(.5) = .375`

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