Question

Find the binomial distribution for flipping a coin 3 times, where "heads" is a success. P(k successes) = nCk pk(1 – p)n – k P(0 successes) = 3C0(0.5)0(0.5)3

Answer 1

0.125, 0.375, 0.375, 0.125

second part is 0.5

Explanation:

Answer 2

0.125, 0.375, 0.375, 0.125

Explanation:

For a binomial distribution :

nCk * p^k * (1 – p)^(n – k)

P(0 successes) = 0 head, k = 0

n = 3 = number of flips

P(success) = 0.5

3C0 * 0.5^0 * 0.5^3

1 * 0.5^0 * 0.5^3 = 0.125

P( 1 success) = 1 head, k = 1

n = 3 = number of flips

P(success) = 0.5

3C1 * 0.5^1 * 0.5^2

3 * 0.5^1 * 0.5^2 = 0.375

P(2 successes) = 2 head, k = 2

n = 3 = number of flips

P(success) = 0.5

3C2 * 0.5^2 * 0.5^1

3 * 0.5^2 * 0.5^1 = 0.375

P(3 successes) = 3 head, k = 3

n = 3 = number of flips

P(success) = 0.5

3C3 * 0.5^3 * 0.5^0

1 * 0.5^3 * 0.5^0 = 0.125