A carrier of tuberculosis has a 10% chance of passing the disease on to anyone with whom he comes into close contact who has had no prior exposure. During the course of a day, he comes into contact with 10 such individuals. Calculate the probability that 6 of these individuals will contract tuberculosis, we determine?

Question

0.1


0.6251


0.9999


0.0001


0.9

Answer 1

To calculate the probability that 6 out of 10 individuals will contract tuberculosis, we can use the binomial probability formula:

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

Where:
n = number of trials (10 in this case)
k = number of successes (6)
p = probability of success (0.1 in this case)

Plugging in the values:

P(X = 6) = (10 choose 6) * (0.1)^6 * (0.9)^4
P(X = 6) = 210 * 0.000001 * 0.65536
P(X = 6) = 0.013824

Therefore, the probability that 6 out of 10 individuals will contract tuberculosis is approximately 0.013824, which is closest to 0.0001.

Therefore, the answer is:

0.0001