Question

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n =8, p = 0.6, P(3 or fewer) Group of answer choices

Answer 1

`P(X \leq 3) = 0.1738`

Explanation:

Binomial probability distribution

The 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).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

In this question, we have that:

`n = 8, p = 0.6`

P(3 or fewer)

`P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)`

In which

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 0) = C_(8,0).(0.6)^(0).(0.4)^(8) = 0.0007`

`P(X = 1) = C_(8,1).(0.6)^(1).(0.4)^(7) = 0.0079`

`P(X = 2) = C_(8,2).(0.6)^(2).(0.4)^(6) = 0.0413`

`P(X = 3) = C_(8,0).(0.6)^(3).(0.4)^(5) = 0.1239`

`P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0007 + 0.0079 + 0.0413 + 0.1239 = 0.1738`