82.0k views
4 votes
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
by
8.8k points

1 Answer

1 vote

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
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories