If x is a binomial random variable, compute p (x) for each of the following cases: P (x) = n! / (x! (n-x) !) * p^x (1-p) ^ (n-x)

is the formula you have to evaluate for each number set.

n=5, x=1, p = 0.2

n=4, x=2, q = 0.4

n=3, x=0, p = 0.7

n=5, x=3, p = 0.1

n=4, x = 2, q = 0.6

n=3, x=1, q = 0.9

P (x) = nCx p^x (1 - p) ^ (n - x) = n! / (x! (n - x) !) * p^x * q^ (n - x)

For n = 5, x = 1, p = 0.2:

P (1) = 5! / (1! (5 - 1) !) * 0.2^1 * (1 - 0.2) ^ (5 - 1) = 5 * 0.2 * 0.4096 = 0.4096

For n = 4, x = 2, q = 0.4:

P (2) = 4! / (2! (4 - 2) !) * (1 - 0.4) ^2 * 0.4^ (4 - 2) = 6 * 0.36 * 0.16 = 0.3456

For n = 3, x = 0, p = 0.7:

P (0) = 3! / (0! (3 - 0) !) * 0.7^0 * (1 - 0.7) ^ (3 - 0) = 1 * 1 * 0.027 = 0.027

For n = 5, x = 3, p = 0.1

P (3) = 5! / (3! (5 - 3) !) * 0.1^3 * (1 - 0.1) ^ (5 - 3) = 10 * 0.001 * 0.81 = 0.0081

For n = 4, x = 2, q = 0.6

P (2) = 4! / (2! (4 - 2) !) * (1 - 0.6) ^2 * 0.6^ (4 - 2) = 6 * 0.16 * 0.36 = 0.3456

For n = 3, x = 1, q = 0.9

P (1) = 3! / (1! (3 - 1) !) * (1 - 0.9) ^1 * 0.9^ (3 - 1) = 3 * 0.1 * 0.81 = 0.243