Question

A doctor sees three patients. The probabilities that patient 1, patient 2 and patient 3 are sick are 0.1, 0.4 and 0.7 respectively. Assume that the sicknesses of patients are independent events.

1.The probability that none of the patients is sick is (rounded to two decimal places):

2.. The probability that exactly one patient is sick is (rounded to two decimal places):

Answer 1

1:

The probability that patient 1 will not sick is

P(patient 1 is not sick) =1 - 0.1 = 0.9

The probability that patient 2 will not sick is

P(patient 2 is not sick) =1 - 0.4 = 0.6

The probability that patient 3 will not sick is

P(patient 3 is not sick) =1 - 0.7 = 0.3

Since each patient is independent from other so the probability that none of the patients is sick is

P(patient 1 is not sick)*P(patient 2 is not sick) * P(patient 3 is not sick) = 0.9 * 0.6 * 0.3 = 0.162

Answer: 0.16

2:

The probability that exactly one patient is sick is

P(patient 1 is not sick)*P(patient 2 is not sick) * P(patient 3 is sick) + P(patient 1 is not sick)*P(patient 2 is sick) * P(patient 3 is not sick) +P(patient 1 is sick)*P(patient 2 is not sick) * P(patient 3 is not sick) = 0.9 * 0.6 * 0.7 + 0.9 * 0.4 * 0.3 +0.1 * 0.6 * 0.3 = 0.504

Answer: 0.50