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.
-$n = 10 , x = 2 , p = 0.5$
A) $0.0439$
B) $0.0571$
C) $0.2500$
D) $0.0659$

Question

Quizplus · Accepted Answer

The probability of x successes in n trials for a binomial distribution is given by $P(X=x) = \binom{n}{x} p^x (1-p)^{n-x}$. For $n = 10$, $x = 2$, and $p = 0.5$, this becomes $P(X=2) = \binom{10}{2} (0.5)^2 (0.5)^{8} = 45 \times 0.00390625 = 0.17578125 \times 0.25 = 0.0439453125$, which rounds to $0.0439$.

Assume That a Procedure Yields a Binomial Distribution with a Trial