compute the probability of x successes in the n independent trials of the expirement.
n=10
p=0.4
x=3
sorry cant help but you could try google
The best way to do this is with a TI83/84 Plus calculator.
The answer is .214990848
To compute the probability of getting exactly x successes in n independent trials of an experiment, we can use the binomial probability formula. The formula is:
P(X = x) = (nCx) * (p^x) * ((1-p)^(n-x))
Where:
- P(X = x) represents the probability of getting exactly x successes.
- nCx is the binomial coefficient, which is the number of ways to choose x success from n trials. It can be calculated using the combination formula:
nCx = n! / (x! * (n-x)!)
- p is the probability of success in a single trial.
- (p^x) represents the probability of getting x successes.
- ((1-p)^(n-x)) represents the probability of getting (n-x) failures.
Using your values:
n = 10
p = 0.4
x = 3
We can compute the probability as follows:
P(X = 3) = (10C3) * (0.4^3) * ((1-0.4)^(10-3))
To find the value of (10C3), we can calculate it using the combination formula:
10C3 = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Plugging in the values into the formula:
P(X = 3) = 120 * (0.4^3) * (0.6^7) = 0.2150 (rounded to four decimal places)
Therefore, the probability of getting exactly 3 successes in 10 independent trials of the experiment is approximately 0.2150.