Binomial Probabilites 1 Interpretaion Suppose you are a hosp

Binomial Probabilites:

1. Interpretaion: Suppose you are a hospital manager and have been told that there is no need to worry tht respirator monitoring equipment might fail because the probability any one monitor will fail is only 0.01. The hospital has 20 such monitors and they work independently. Should you be more concerned about the probability that exactly one of the 20 monitors fails, or that at least one fails? Explain.

2. Critical Thinking: In a experiment, there are n independent trials. For each trial, there are three outcomes, A, B, and C. For each trial, the probability of outcome A is 0.40; the probability of outcome B is 0.50; and the probability of outcome c is 0.10. Suppose there are 10 trials.

a) Can we use the binomial experiment model to determine the probability of four outcomes of type A, five of type B, and one of type C? Please explain.

b) Can we use the binomial experiment model to determine the probability of four outcome of type A and six outcomes that are not type A? Explain. What is the probability of success on each trial?

Solution

Answer to question# 1)

When 1 respirator fails , their are 19 more working

We got:

n = 20

p = 0.01

.

Binomial probability formula is:

P(X=x) = nCx * p^x * (1-p)^n-x

P(x=1) = 20C1 * 0.01^1 * 0.99^19 = 0.1652

.

P(at least one fails) = 1 - P(none fails)

P(none fails) = P(x=0)

P(x=0) = 20C0 * 0.01^0 * 0.99^20 = 0.8179

P(at least one fails) = 1 - 0.8179

P(at least one fails) = 0.1821

.

Thus probability of 1 failing is 0.1652 which is less than the probability of at least one failing 0.1821. Thus the hospital manager must be more concerned about at least 1 respirator failing