You are performing 5 independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of at least three successes. Round your answer to four decimal places if necessary.
A)0.9421
B) 0.9997
C) 0.0579
D) 0.9933
E) 0.0410

Question

You are performing 5 independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of at least three successes. Round your answer to four decimal places if necessary.  
A)0.9421
B) 0.9997
C) 0.0579
D) 0.9933
E) 0.0410

Quizplus · Accepted Answer

The probability of at least three successes in 5 independent Bernoulli trials with $p = 0.8$ can be calculated using the binomial distribution formula: $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$, where $n = 5$, $p = 0.8$, and $k$ is the number of successes. We calculate the probabilities for 3, 4, and 5 successes and sum them up: $P(X \geq 3) = P(X=3) + P(X=4) + P(X=5)$. This calculation results in a probability of 0.9421, indicating that there's a 94.21% chance of getting at least three successes.

You Are Performing 5 Independent Bernoulli Trials With p=0.8p = 0.8p=0.8

You Are Performing 5 Independent Bernoulli Trials With $p = 0.8$