Question

3, A hospital is treating patients who have Lhassa Fever, 70% of patients with this disease die, and each patient lives or dies independently of other patients. a. If there are currently 12 Lhassa Fever patients in the hospital, find the probability that6 or fewer die. b. If there are currently 12 Lhassa Fever patients in the hospital, find the probability that 6 or more die. If the hospital has 8 Lhassa Fever patients, find the probability that all die. If the hospital has 8 Lhassa Fever patients, find the probability that 7 or 8 die. c. d.

Answer 1

Binomial distribution

P(X= x) = nCx p^x q^n-x

p = 0.7

q = 1 - p = 0.3

a) n = 12

P(6 ofr fewer will die) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6)

= 0.3¹² + 12x0.7x0.3¹¹ + 12C2x0.7²x0.3¹⁰ + 12C3x0.7³x0.3⁹ + 12C4x0.7⁴x0.3⁸ + 12C5x0.7⁵x0.3⁷ + 12C6x0.7⁶x0.3⁶

= 0.00000 + 0.00001 + 0.00019 + 0.00149 + 0.00780 + 0.02911 + 0.07925

= 0.11785

b) P(6 or more will die) = 1 - P(5 or less will die)

= 1 - [P(0) + P(1) + P(2) + P(3) + P(4) + P(5)]

= 1 - (0.00000 + 0.00001 + 0.00019 + 0.00149 + 0.00780 + 0.02911)

= 0.91126

c) P(all 8 will die) = 0.7⁸

= 0.05764

d) P(7 or 8 die) = P(7) + P(8)

= 8x0.7⁷x0.3 + 0.7⁸

= 0.19765 + 0.05764

= 0.25530