f x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?Select one:a..0055.b..0063.c..124.d..232.e..994.
Question
f x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?Select one:a..0055.b..0063.c..124.d..232.e..994.
Solution
To solve this problem, we need to use the formula for the binomial probability, which is:
P(X = x) = C(n, x) * (p^x) * ((1-p)^(n-x))
where:
- P(X = x) is the probability we are trying to find,
- C(n, x) is the combination of n items taken x at a time,
- p is the probability of success,
- n is the number of trials, and
- x is the number of successes.
Given in the problem, we have n = 10, p = 0.8, and x = 4.
First, calculate C(n, x) = C(10, 4). This is the number of ways to choose 4 successes out of 10 trials. Using the formula for combinations, we get C(10, 4) = 10! / [4!(10-4)!] = 210.
Next, calculate (p^x) = (0.8^4) = 0.4096.
Then, calculate ((1-p)^(n-x)) = ((1-0.8)^(10-4)) = (0.2^6) = 0.000064.
Finally, multiply these three values together to get the probability:
P(X = 4) = 210 * 0.4096 * 0.000064 = 0.0055.
So, the answer is a. 0.0055.
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