Answer:
21. Option d
22. Option b
23. Option b
Step-by-step explanation:
The formula to calculate the binomial probability is represented as follows.
[tex]P(X=x) = \frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}[/tex]
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 [tex]P(X=3) = \frac{6!}{3!(6-3)!}(0.35)^3(1-0.35)^{6-3}\\\\P(3) = 0.2354[/tex]
Option d.
2. Second we are asked to calculate the probability of obtaining 5 successes, with n = 20 and p = 60%, p = 0.6.
[tex]P(X=5) = \frac{20!}{5!(20-5)!}(0.6)^5(1-0.6)^{20-5}\\\\P(5) = 0.00129[/tex]
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.
[tex]P(X=2) = \frac{10!}{2!(10-2)!}(0.5)^2(1-0.5)^{10-2}\\\\P(2) = 0.04394[/tex]
option b
