x is a binomial random variable. (Give your answers correct to three decimal pla

Question

x is a binomial random variable. (Give your answers correct to three decimal places.)

(a) Calculate the probability of x for:    n = 7,    x = 6,    p = 0.25
P(x) =  

(b) Calculate the probability of x for:    n = 6,    x = 5,    p = 0.5
P(x) =  

(c) Calculate the probability of x for:    n = 7,    x = 6,    p = 0.85
P(x) =  

(d) Calculate the probability of x for:    n = 4,    x = 2,    p = 0.2
P(x) =  

(e) Calculate the probability of x for:    n = 6,    x = 3,    p = 0.1
P(x) =  

(f) Calculate the probability of x for:    n = 5,    x = 3,    p = 0.7
P(x) =

Explanation / Answer

Solution:

(a) Calculate the probability of x for: n = 7, x = 6, p = 0.25
P(x) = P(x= 6) = 7C6 (0.25)^6 (0.75)^7-6
= 0.0012817
(b) Calculate the probability of x for: n = 6, x = 5, p = 0.5
P(x) = P(x = 5)
P(x = 5) = 6C5 (0.5)^5 (0.5)^6-5
= 0.0937500
(c) Calculate the probability of x for: n = 7, x = 6, p = 0.85
P(x) = P(x = 6)
P(x = 6) = 7C6 (0.85)^6 (0.15)^7-6
= 0.3960070
(d) Calculate the probability of x for: n = 4, x = 2, p = 0.2
P(x) = P(x = 2)
P(x = 2) = 4C2 (0.2)^2 (0.8)^4-2
= 0.1536000
(e) Calculate the probability of x for: n = 6, x = 3, p = 0.1
P(x) = P(x = 3)
P(x = 3) = 6C3 (0.1)^3 (0.9)^6-3
= 0.0145800
(f) Calculate the probability of x for: n = 5, x = 3, p = 0.7
P(x) = P(x = 3)
P(x = 3) = 5C3 (0.7)^3 (0.3)^5-3
= 0.3087000

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