Consider a Bernoulli experiment with $n = 5$ and $p = 0.4$ . What is $P ( X = 3 )$ ?
Round your answer to five decimal places if necessary.
A) 0.02304
B) 0.3456
C) 0.03456
D) 0.0008
E) 0.2304

Question

Consider a Bernoulli experiment with $n = 5$ and $p = 0.4$ . What is $P ( X = 3 )$ ?
  Round your answer to five decimal places if necessary.
A) 0.02304
B)  0.3456
C)  0.03456
D)  0.0008
E)  0.2304

Quizplus · Accepted Answer

The probability of exactly $k$ successes in $n$ Bernoulli trials is given by the binomial probability formula: $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$. For $n = 5$, $k = 3$, and $p = 0.4$, this calculates to $P(X = 3) = \binom{5}{3} (0.4)^3 (0.6)^2 = 10 \times 0.064 \times 0.36 = 0.2304$.

Consider a Bernoulli Experiment With n=5n = 5n=5 And p=0.4p = 0.4p=0.4

Consider a Bernoulli Experiment With $n = 5$ And $p = 0.4$