You are performing 5 independent Bernoulli trials with $p = 0.6$ and $q = 0.4$ . Calculate the probability that it will be at most 2 successes. Round your answer to five decimal places if necessary.
A) 0.31744
B) 0.02304
C) 0.06912
D) 0.1
E) 0.7696

Question

You are performing 5 independent Bernoulli trials with $p = 0.6$ and $q = 0.4$ . Calculate the probability that it will be at most 2 successes. Round your answer to five decimal places if necessary.  
A) 0.31744
B)  0.02304
C)  0.06912
D)  0.1
E)  0.7696

Quizplus · Accepted Answer

The probability of at most 2 successes in 5 independent Bernoulli trials with $p = 0.6$ and $q = 0.4$ can be calculated using the binomial distribution formula: $P(X = k) = \binom{n}{k} p^k q^{(n-k)}$, where $n = 5$, $p = 0.6$, and $q = 0.4$. We calculate for $k = 0, 1, 2$ and sum these probabilities.For $k = 0$: $P(X = 0) = \binom{5}{0} (0.6)^0 (0.4)^5 = 0.01024$For $k = 1$: $P(X = 1) = \binom{5}{1} (0.6)^1 (0.4)^4 = 0.0768$For $k = 2$: $P(X = 2) = \binom{5}{2} (0.6)^2 (0.4)^3 = 0.2304$Summing these probabilities gives $0.01024 + 0.0768 + 0.2304 = 0.31744$.

You Are Performing 5 Independent Bernoulli Trials With p=0.6p = 0.6p=0.6

You Are Performing 5 Independent Bernoulli Trials With $p = 0.6$