Question

Consider a binomial experiment with 4 trials and p = 0.7. Compute the probability of 1 success, f(1). If required, round your answer to two decimal places. f(1) = Compute f(0). If required, round your answer to two decimal places. f(0) = Compute f(2). If required, round your answer to two decimal places. f(2) = Find the probability of at least one success. If required, round your answer to two decimal places. P(x ≥ 1) = Find the expected value, variance, and standard deviation. If required, round your answers to two decimal places. Expected value = Variance = Standard deviation =

Answer 1

Answer with Step-by-step explanation:

For a given Binomial event with  probability of success 'p' the probabolity of 'r' success in 'n' trails is given by

$P(E)=\frac{n!}{(n-r)!\cdot r!}p^r\cdot (1-p)^{n-r}$

Thus for given 4 trails (n = 4) we have

Part 1)

Probability of 1 success is  

$P(E_1)=\frac{4!}{(4-1)!\cdot 1!}\cdot 0.7^1\cdot (1-0.7)^{4-1}\\\\\therefore P(E_1)=0.076$

Part 2)

Probability of 2 successes

$P(E_2)=\frac{4!}{(4-2)!\cdot 2!}\cdot 0.7^2\cdot (1-0.7)^{4-2}\\\\\therefore P(E_2)=0.265$

Part 3)

Probability of at least 1 success

$P(E)=1-(1-p)^n\\\\\therefore P(E_3)=1-(1-0.7)^{4}=0.992$