This document discusses using discrete probability distributions to calculate the likelihood of different COVID-19 scenarios. It provides the probabilities of: (a) Exactly 2 people dying out of 15 who are affected, using the binomial distribution. (b) The 10th affected person dying, using the geometric distribution. (c) The 10th affected person being the 5th to die, using the negative binomial distribution.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
COVID-19
WITH
DISCRETE PROBABILITY DISTRIBUTIONS

2. Example-20
If the probability that a person will die by COVID-19 in
China is 0.06 (Till 2nd May 2020 by W.H.O.).
What is the probability that
(a) Exactly 2 effected persons will die out of 15.
(b) The 10th effected person will die.
(c) The 10th effected person will be the 5th person to die.

3. Solution:
Let x denotes the number of a person who effects by COVID-19,
Then the number of a person who dies it, will be considered a
success.
(a) There are 15 persons with two possible outcomes will die or
will not die, the probability is constant and trials are
independent, therefore the binomial distribution is suitable.
Where n = 15, P = 0.06, q = 0.94, x = 2
𝑃 𝑥 = 𝑥 = 𝑛
𝑐 𝑥 𝑝 𝑥 𝑞 𝑛−𝑥
𝑃 𝑥 = 2 = 15
𝑐2 0.06 2
0.94 15−2
= 0.1691

4. (b)Since the 10th person is the first to die, So the first success occurs on
the 10th , therefore the geometric distribution is suitable.
Where P = 0.06, q = 0.94, x = 10
𝑃 𝑥 = 10 = (𝑝)(𝑞) 𝑥−1
𝑃 𝑥 = 10 = 0.06 0.94 10−1
= 0.0344
(c)Since 10th person effected by COVID-19 will be the 5th to die implies
that the 5th success occurs the 10th trial, therefore the negative
binomial distribution is suitable.
Where x = 10, k = 5, p = 0.06, q = 0.94
𝑃 𝑋 = 𝑥 =
𝑥 − 1
𝑘 − 1
𝑝 𝑘 𝑞 𝑥−𝑘
𝑃 𝑋 = 10 =
10 − 1
5 − 1
(0.06)5 (0.94)10−5 = 0.000072