find the probability that atmost 5 such patients recently admitted to hospital are chain smokers? solve by using binomial distribution

To solve this problem using the binomial distribution, we need to know two things: the total number of patients recently admitted to the hospital (n) and the probability that any given patient is a chain smoker (p).

The binomial distribution formula is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

Where:

• P(X=k) is the probability of k successes in n trials
• C(n, k) is the combination of n items taken k at a time
• p is the probability of success on an individual trial
• (1-p) is the probability of failure on an individual trial

To find the probability that at most 5 patients are chain smokers, we need to find the sum of the probabilities that exactly 0, 1, 2, 3, 4, and 5 patients are chain smokers.

So, P(X<=5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

Without the values of n and p,