Suppose that X is a binomial random variable with n=10 and p=.29 Find P(2).
Write only a number as your answer. Round to 4 decimal places (for example 0.1489)
To find P(2) for a binomial random variable, we use the binomial probability formula. The formula is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
In this formula, n represents the number of trials, p represents the probability of success, x represents the number of successes we are interested in, and P(x) is the probability of getting x successes.
In this case, n = 10, p = 0.29, and x = 2.
Using the formula, we can calculate P(2) as follows:
P(2) = (10C2) * 0.29^2 * (1-0.29)^(10-2)
To calculate (10C2), we use the combination formula:
(10C2) = 10! / (2! * (10-2)!)
= 10! / (2! * 8!)
= (10 * 9) / (2 * 1)
= 90 / 2
= 45
Substituting these values into the binomial probability formula:
P(2) = 45 * 0.29^2 * (1-0.29)^(10-2)
= 45 * 0.0841 * 0.5369
= 1.525805
Rounding this to 4 decimal places, P(2) is approximately 1.5258.
To find P(2), we can use the formula for the probability mass function (PMF) of a binomial random variable.
The formula is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where n is the number of trials, p is the probability of success in each trial, and k is the number of successes we want to find the probability for.
In this case, n = 10, p = 0.29, and k = 2. Let's substitute these values into the formula:
P(2) = (10 choose 2) * (0.29)^2 * (1 - 0.29)^(10 - 2)
Using the combination formula (n choose k) = n! / (k! * (n - k)!), we can calculate:
P(2) = (10! / (2! * (10 - 2)!)) * (0.29)^2 * (0.71)^8
Calculating the factorials:
P(2) = (10 * 9) / (2 * 1) * (0.29)^2 * (0.71)^8
P(2) = 45 * 0.0841 * 0.0881
Multiplying the values:
P(2) = 0.3336
Rounding to 4 decimal places:
P(2) â 0.3336
Therefore, the answer is 0.3336.