Question

Determine the following:

Answer 1

Answer:

a) P(X = 0) = 0.5997

b) P(X = 9) = 0.0016

c) P(X = 8) = 0.0047

d) P(X = 5) = 0.4018

Step-by-step explanation:

These following problem are examples of the binomial probability distribution.

Binomial probability

Th binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

(a) for n = 4 and π = 0.12, what is P(X = 0)?

$P(X = 0) = C_{4,0}.(0.12)^{0}.(0.88)^{4} = 0.5997$

(b) for n = 10 and π = 0.40, what is P(X = 9)?

$P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016$

(c) for n = 10 and π = 0.50, what is P(X = 8)?

$P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0047$

(d) for n = 6 and π = 0.83, what is P(X = 5)?

$P(X = 5) = C_{6,5}.(0.83)^{5}.(0.17)^{1} = 0.4018$