Question

Calculate each binomial probability: (a) X = 1, n = 7, π = 0.50 (Round your answer to 4 decimal places.) P(X = 1) (b) X = 3, n = 6, π = 0.20 (Round your answer to 4 decimal places.) P(X = 3) (c) X = 4, n = 16, π = 0.70 (Round your answer to 4 decimal places.) P(X = 4)

Answer 1

Solution

Given that ,

a) p = 0.50

1 - p = 1 - 0.50 = 0.50

n = 7

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 1 ) = (₇C ₁) * (0.50)¹ * (0.50)⁶

= 0.0546875

Probability = 0.0547

b) p = 0.20

1 - p = 1 - 0.20 = 0.80

n = 6

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 3 ) = (₆C ₃) * (0.20)³ * (0.80)³

= 0.08192

Probability = 0.0819

c) p = 0.70

1 - p = 1 - 0.70 = 0.30

n = 16

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 4 ) = (₁₆C ₄) * (0.70)⁴ * (0.30)¹²

= 0.0002322

Probability = 0.0002