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?
0.1
0.6251
0.9999
0.0001
0.9
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