Question

Consider a binomial probability distribution with p = 0.2. Complete parts a through c below. a. Determine the probability of exactly three successes when n = 4. P(3) = 0.0256 (Round to four decimal places as needed.) b. Determine the probability of exactly three successes when n = 6. P(3) = 0.082 (Round to four decimal places as needed.) c. Determine the probability of exactly three successes when n = 7 P(3) = 0.1147 (Round to four decimal places as needed.)

The answers are in red. I just want to know how to correctly solve this...

Answer 1

Answer:

Given that:

Consider a binomial probability distribution with p=0.2

p = 0.2

1 - p = 1 - 0.2 = 0.8

(a)  Determine the probability of exactly three successes when n=4.

n = 4

Using binomial probability formula ,

P(X = 1) =
(ⁿ C _x)
p' (1-pn-1

P(X = 3) =
(⁴ C ₃)
(0.2) (0.8)

P(X = 3) = 4 * 0.008 * 0.8

P(X = 3) = 0.0256

probability = 0.0256

(b)  Determine the probability of exactly three successes when n=6

n = 6

Using binomial probability formula ,

P(X = 1) =
(ⁿ C _x)
p' (1-pn-1

P(X = 3) =
(⁶ C ₃)
(0.2)-(0.8)

P(X =3) = 20 * 0.008* 0.512

P(X = 3) = 0.0819

probability = 0.0819

(c) Determine the probability of exactly three successes when n= 7

n = 7

Using binomial probability formula ,

P(X = 1) =
(ⁿ C _x)
p' (1-pn-1

P(X = 3) =
(⁷ C ₃)
(0.2) (0.8)

P(X =3) = 35 * 0.008 * 0.4096

P(X = 3) = 0.1146

probability = 0.1146

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