Question

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 12, p = 0.6, P(Fewer than 4)

Answer 1

`P(x < 4) = 0.0152`

Explanation:

We are given a binomial distribution.

P(Success) = p = 0.6

We can calculate probability as:

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 12

We have to evaluate:

`P(x < 4) \\= P(x = 0) + P(x = 1) + P(x = 2)+P(x = 4) \\= \binom{12}{0}(0.6)^0(1-0.6)^(12) +...+ \binom{12}{3}(0.6)^3(1-0.6)^(9)\\= 0.00001+0.0003+0.0024+0.01245\\= 0.0152`

0.0152 is the required probability.