Answer:
P(X = 2) = 0.27894
Step-by-step explanation:
Given:
- The probability that no vision correction is required p = 0.23
- No. adults are randomly selected n = 6
Find:
- P ( Exactly 2 dont require vision correction)
Solution:
- We will declare a random variable X is the umber of adults out of 6 that do not require vision correction. X follows a Binomial distribution:
X~ B ( 6 , 0.23 )
- The probability required is P ( X = 2 )
- Using the pmf of binomial distribution we have:
P(X = 2) = 6C2 * (0.23)^2 * (0.77)^4
P(X = 2) = 15 * 0.0529 * 0.35153041
P(X = 2) = 0.27894
The probability that exactly 2 out of the 6 adults do not require vision correction is:
P = 0.16
We know that, for a random adult:
Then, the probability that 2 out of 6 adults do not need vision correction is:
P = C(6, 2)*(0.23)^2*(0.67)^4
Where C(6, 2) represents the different groups of 2 that we can make out of the whole group of 6 adults.
Such that:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Then for our case:
[tex]C(6, 2) = \frac{6!}{(6 - 2)!*2!} = \frac{6*5}{2} = 15[/tex]
So out of these 6 adults, there can be made 15 different groups.
Then the probability is:
P = 15*(0.23)^2*(0.67)^4 = 0.16
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
