If x is a binomial random variable, calculate the probability of x for each case.
n=4, x=1, p=0.3 answer 0.4116
Correct!
To calculate the probability of a binomial random variable, you can use the formula:
P(x) = (nCx) * p^x * (1-p)^(n-x)
In this case, n = 4, x = 1, and p = 0.3.
Let's calculate it step-by-step:
1. Calculate the binomial coefficient (nCx):
The binomial coefficient represents the number of ways to choose x successes from n trials. It can be calculated using the formula:
(nCx) = n! / (x!(n-x)!)
In this case, (4C1) = 4! / (1!(4-1)!) = 4! / (1! * 3!) = 4.
2. Calculate p^x:
In this case, p = 0.3 and x = 1, so p^x = 0.3^1 = 0.3.
3. Calculate (1-p)^(n-x):
In this case, (1-p) = (1-0.3) = 0.7, and (n-x) = (4-1) = 3, so (1-p)^(n-x) = 0.7^3 = 0.343.
4. Multiply the three values together:
P(x) = (nCx) * p^x * (1-p)^(n-x) = 4 * 0.3 * 0.343 = 0.4116.
So the probability of x = 1 when n = 4 and p = 0.3 is 0.4116.