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 =

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InesWalston InesWalston · Answer 1 · 2019-09-27T09:48:31+02:00

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

[tex]P(E)=\frac{n!}{(n-r)!\cdot r!}p^r\cdot (1-p)^{n-r}[/tex]

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

Part 1)

Probability of 1 success is

[tex]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[/tex]

Part 2)

Probability of 2 successes

[tex]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[/tex]

Part 3)

Probability of at least 1 success

[tex]P(E)=1-(1-p)^n\\\\\therefore P(E_3)=1-(1-0.7)^{4}=0.992[/tex]