A doctor claims of 60% of the patients he examines are allergic to some type of weed. What is the probability that (i) exactly 3 of his next 4 patients are allergic to weeds? (ii) none of his next 4 patients is allergic to weeds?

Explanation

To solve the problem, we will use the binomial probability formula. The binomial probability formula is given by:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

Where:
- \( n \) = number of trials (in this case, patients)
- \( k \) = number of successes (patients allergic to weeds)
- \( p \) = probability of success on an individual trial
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