This is simple for you, hard for me

[mgibel]

This is simple for you, hard for me...

I really need to know how to do a question like this for a course I am taking. Can you help?

Out of 2 million hay fever sufferers in Canada, 82% are allergic to ragweed. If a random sample of 7 hay fever sufferers is selected,

a) what is the probability that 3 are allergic to ragweed?

b) What is the probability that 1 is allergic to ragweed?


What is the formula?

 

[mathman]

The basic idea is to use the binomial distribution with p=.82 and q=.18.
That is expand (p+q)ⁿ into powers of p (and q).
Then the probability of exactly k yesses is {n,k}p^kq^n-k.
I am using {n,k} to represent n!/k!(n-k)!. In your problem, n=7 and k=1 or k=3.

 

[tacman]

I completely understand how this question can seem simple for me, but difficult for you. Probability and statistics can be challenging topics for many people. However, with some practice and understanding of the formulas, you can also find it simple.

To answer your question, let's break it down step by step. In order to solve this problem, we need to use the binomial distribution formula, which is P(x) = nCx * p^x * (1-p)^(n-x), where n is the sample size, x is the number of successes, and p is the probability of success.

a) In this case, n = 7 (since we have a random sample of 7 hay fever sufferers) and p = 0.82 (since 82% of hay fever sufferers are allergic to ragweed). We are looking for the probability that 3 out of 7 are allergic to ragweed, so x = 3. Plugging these values into the formula, we get:

P(3) = 7C3 * 0.82^3 * (1-0.82)^(7-3) = 0.339

Therefore, the probability that 3 out of 7 hay fever sufferers in the sample are allergic to ragweed is 0.339 or 33.9%.

b) Similarly, for the second part of the question, we are looking for the probability that 1 out of 7 is allergic to ragweed. So, x = 1 and plugging in the values, we get:

P(1) = 7C1 * 0.82^1 * (1-0.82)^(7-1) = 0.033

Therefore, the probability that 1 out of 7 hay fever sufferers in the sample is allergic to ragweed is 0.033 or 3.3%.

I hope this explanation helps you understand the problem and the formula used to solve it. Remember, practice makes perfect and I am sure with some more practice, you will find probability and statistics to be simple as well. Best of luck with your course!