Question

Determine the binomial probability

Answer 1

21. Option d

22. Option b

23. Option b

Explanation:

The formula to calculate the binomial probability is represented as follows.

`P(X=x) = (n!)/(x!(n-x)!)p^x(1-p)^(n-x)`

The formula to calculate the binomial probability is represented as follows.

In this formula x represents the number of successes, n represents the number of times the experiment is repeated, p represents the probability of success.

1. First we are asked to calculate the probability of obtaining 3 successes, with n = 6 and p = 0.35.

Then we substitute the values in the formula
`P(X=3) = (6!)/(3!(6-3)!)(0.35)^3(1-0.35)^(6-3)\\\\P(3) = 0.2354`

Option d.

2. Second we are asked to calculate the probability of obtaining 5 successes, with n = 20 and p = 60%, p = 0.6.

`P(X=5) = (20!)/(5!(20-5)!)(0.6)^5(1-0.6)^(20-5)\\\\P(5) = 0.00129`

option b

3. Third we are asked to calculate the probability of obtaining 2 successes, with n = 10 and p = 1/2, p = 0.5.

`P(X=2) = (10!)/(2!(10-2)!)(0.5)^2(1-0.5)^(10-2)\\\\P(2) = 0.04394`

option b