Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal
places.
-$\mathrm { n } = 4 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 6 }$

A) 0.012
B) 0.015
C) 0.004
D) 0.023

Question

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal
places.
-$\mathrm { n } = 4 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 6 }$

A) 0.012
B) 0.015
C) 0.004
D) 0.023

Quizplus · Accepted Answer

The binomial probability formula is $ P(X = x) = \binom{n}{x} p^x (1-p)^{n-x} $. For $ n = 4 $, $ x = 3 $, and $ p = \frac{1}{6} $, the calculation is $ \binom{4}{3} \left(\frac{1}{6}\right)^3 \left(\frac{5}{6}\right)^1 = 4 \times \frac{1}{216} \times \frac{5}{6} = 0.015 $.

Assume That a Procedure Yields a Binomial Distribution with a Trial