You are performing 5 independent Bernoulli trials with p 3

You are performing 5 independent Bernoulli trials with p = .3 and q = .7. Calculate the probability of the stated outcome. Check your answer using technology. (Round your answer to four decimal places.)

At most three successes

P(X  3) = ___________

Solution

P(X 3) =P(X=0)+P(X=1)+P(X=2)+P(X=3)

P(X 3) =(⁵C₀)(0.3)^o(0.7)⁵+(⁵C₁)(0.3)¹(0.7)⁴+(⁵C₂)(0.3)²(0.7)³+(⁵C₃)(0.3)³(0.7)²

P(X 3) =0.16807+0.36015+0.30870+0.13230

P(X 3) =0.96922