URGENT! In a school, 8% of students are left handed. If 50 classes of 20 students are randomly selected, what is the probability of 10 classes have no left handed students?
I know that this is a binomial distribution question, but I can't seem to do this question even though I can apply the equation to simpler questions. Help is very much appreciated. Thank you!
prob(left) = .08
prob(right) = .92
let's first do the prob that in a class of 20 nobody is left-handed
= C(20,0)(.08)^0 (.92)^10
= .434388.. (I stored it)
or prob(1 or more lefthanders) = 1-.4343...= .56561...
Now we want the prob that of 50 classes contain no left-handed students
= C(50,10) (.4343..)^10 (.56561..)^40
= .0003099
I assumed you wanted exactly 10 of the 50 classes to contain no left-handers
Yes, I want exactly 10 of the 50 classes to contain no left handers.
So, instead of using .08 as the p for the last part, I should use the probability found from no left handers in a class of 20 instead? The question did ask me to find this as well, although I didn't put it up here as I have no problem solving it.
Thank you for the time and effort used to answer this question. I really appreciate it.
To solve this problem, we can use the binomial distribution formula.
The binomial distribution formula is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes in n trials
- C(n, k) is the combination formula, denoting the number of ways to choose k items from a set of n items
- p is the probability of success on an individual trial
- (1 - p) is the probability of failure on an individual trial
- n is the number of trials
In this case, we want to find the probability of 10 classes having no left-handed students. Let's go step by step to calculate it.
Step 1: Define the variables
In this problem, we have:
- n (number of classes) = 50
- k (number of classes with no left-handed students) = 10
- p (probability of a class having no left-handed students) = 1 - 0.08 (since 8% of students are left-handed)
- q (probability of a class having at least one left-handed student) = 0.08
Step 2: Calculate the probability
Plug the values into the binomial distribution formula:
P(X = 10) = C(50, 10) * (1 - 0.08)^10 * 0.08^(50-10)
Using a calculator or statistical software, we can calculate C(50, 10) = 10272278170.
P(X = 10) = 10272278170 * (0.92)^10 * (0.08)^40
Finally, calculate P(X = 10) using the values we obtained.
Please note that the calculation involves large numbers, so it might be easier to use a calculator or a statistical software to compute the exact value.