A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. The probability of x less than or equals 3 is ____.
n=9, p =0.9, x less than or equals 3.
solution
Given that ,
p = 0.9
1 - p = 1 - 0.9 = 0.1
n = 9
Using binomial probability formula ,
P(X = x) = (n C x) * px * (1 - p)n - x
P(X < 3 ) = P(X=0) +P(X=1)+P(X=2)+P(X=3)
= (9 C 0) * 0.90 * (0.1)9+(9 C 1) * 0.91 * (0.1)8+(9 C 2) * 0.92 * (0.1)7+(9 C 3) * 0.93 * (0.1)6
probability =0.00006
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