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If you flip a fair coin 6 times, what is the probability that you will get exactly 2 heads? p(exactly two heads)

User Sjbuysse
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1 Answer

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Final answer:

The probability of getting exactly 2 heads when flipping a fair coin 6 times is 0.09375, or 9.375%.

Step-by-step explanation:

To find the probability of getting exactly 2 heads when flipping a fair coin 6 times, we can use the binomial probability formula.

Using the binomial probability formula: P(x) = (nCx) * p^x * q^(n-x)

Where:

  • P(x) is the probability of getting exactly x successes (in this case, heads)
  • n is the number of trials (flips)
  • x is the number of successes we want (2 heads)
  • p is the probability of success (getting a head, which is 0.5 for a fair coin)
  • q is the probability of failure (getting a tail, which is also 0.5 for a fair coin)

Plugging in the values: P(2) = (6C2) * (0.5)^2 * (0.5)^(6-2)

Simplifying:

  • Using combinations: P(2) = (6! / (2! * (6-2)!)) * (0.5)^2 * (0.5)^(6-2)
  • Calculating: P(2) = 15 * 0.25 * 0.25 = 0.09375

Therefore, the probability of getting exactly 2 heads when flipping a fair coin 6 times is 0.09375, or 9.375%.

User KWondra
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