Question

You are performing 7 independent Bernoulli trials with p = 0.2 and q = 0.8. Calculate the probability of the stated outcome. Check your answer using technology. (Round your answer to five decimal places.) 

P(X≥3) = _______ 

Answer 1

n = 7 , p = 0.2

P(X) = ⁿc_x p^x ( 1 - p)^n-x

So,

P( X >= 3) = 1 - P( X <= 2)

= 1 - [ P (x = 0) + P( X = 1) + P (X = 2) ]

= 1 - [ ⁷C₀ 0.2⁰ 0.8⁷ + ⁷C₁ 0.2¹ 0.8⁶ + ⁷C₂ 0.2² 0.8⁶ ]

= 0.14803