Question

Determine the following probabilities.

a. For n=6 and (pie sign) = 0.15, what is P(X=0)

b. For n=10 and (pie sign) = 0.30, what is P(X=9)

c. For n=10 and (pie sign) = 0.50, what is P(X=8)

d. For n=3 and (pie sign) = 0.83, what is P(X=2)

Answer 1

a)
Here, n = 6, p = 0.15, (1 - p) = 0.85 and x = 0
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 0)
P(X = 0) = 6C0 * 0.15^0 * 0.85^6
P(X = 0) = 0.3771
0

b)

Here, n = 10, p = 0.3, (1 - p) = 0.7 and x = 9
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 9)
P(X = 9) = 10C9 * 0.3^9 * 0.7^1
P(X = 9) = 0.0001

c)

Here, n = 10, p = 0.5, (1 - p) = 0.5 and x = 8
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 8)
P(X = 8) = 10C8 * 0.5^8 * 0.5^2
P(X = 8) = 0.0439

d)

Here, n = 3, p = 0.83, (1 - p) = 0.17 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 2)
P(X = 2) = 3C2 * 0.83^2 * 0.17^1
P(X = 2) = 0.3513
0