This is simple for you, hard for me

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SUMMARY

The discussion focuses on calculating probabilities using the binomial distribution for a sample of hay fever sufferers in Canada. Specifically, it addresses the scenario where 82% of 2 million sufferers are allergic to ragweed. The formula for the binomial probability is defined as {n,k}p^kq^(n-k), where n represents the sample size (7), k represents the number of successes (1 or 3), p is the probability of success (0.82), and q is the probability of failure (0.18). The participants confirm the application of this formula to find the probabilities for the specified values of k.

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  • Understanding of binomial distribution
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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?
 
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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}pkqn-k.
I am using {n,k} to represent n!/k!(n-k)!. In your problem, n=7 and k=1 or k=3.
 

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