Question

In: Statistics and Probability

the probability that a worker with occupational exposure to dust contracts a lung disease is 0.2....

the probability that a worker with occupational exposure to dust contracts a lung disease is 0.2. three such workers are checked at random. find the probability that

a. none of the three workers contracted a lung disease.

b. at least one of them contracted a lung disease

Solutions

Expert Solution

The asked probability that a worker contracts a lung disease is calculated using a Binomial probability distribution.

Let X be the binomial random variable.

X: Number of workers who contract a lung disease.

Then X has a binomial distribution and the formula for the probability of observing exactly x successes in n trials is given by:

where,

n : number of trials
x : number of successes among n trials
p : the probability of success on a single trial

Given: (the probability that a worker contracts a lung disease is 0.2)

(a) To find the probability that none of the three workers contracted a lung disease.

So, the probability that none of the workers out of three contracted a lung disease is 0.512

(b) Now the probability that at least one of them contracted a lung disease-

So, the probability that at least one of them is contracted to lung disease is 0.488

orchestra answered 2 years ago
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