SOLUTION: Consider a binomial random variable with n = 9 and p = 0.6. Let x be the number of successes in the sample. Evaluate the probability. (Round your answer to three decimal places.)

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Question 1206636: Consider a binomial random variable with n = 9 and p = 0.6. Let x be the number of successes in the sample. Evaluate the probability. (Round your answer to three decimal places.)
P(x ≥ 3)
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Consider a binomial random variable with n = 9 and p = 0.6. Let x be the
number of successes in the sample. Evaluate the probability. (Round your
answer to three decimal places.)
P(x ≥ 3)
It is much easier to calculate P(x=0), P(x=1), P(x=2) and subtract their sum
from 1:

P%28x=0%29%22%22=%22%22%22C%289%2C0%29%22%2A0.6%5E0%2A%281-0.6%29%5E%289-0%29%22%22=%22%22%281%29%281%29%280.4%29%5E9%22%22=%22%220.000262144
P%28x=1%29%22%22=%22%22%22C%289%2C1%29%22%2A0.6%5E1%2A%281-0.6%29%5E%289-1%29%22%22=%22%22%289%29%280.6%29%280.4%29%5E8%22%22=%22%220.003538944
P%28x=2%29%22%22=%22%22%22C%289%2C2%29%22%2A0.6%5E2%2A%281-0.6%29%5E%289-2%29%22%22=%22%22%2836%29%280.6%29%5E2%280.4%29%5E7%22%22=%22%220.021233664

P%28x%3C3%29%22%22=%22%22P%28x=0%29%2BP%28x=1%29%2BP%28x=2%29%22%22=%22%220.000262144%2B0.003538944%2B0.021233664%22%22=%22%220.025034752

P%28x%3E=3%29%22%22=%22%221-P%28x%3C3%29%22%22=%22%221-0.025034752%22%22=%22%220.974965248

Round to 0.975
 
Edwin