Question

20 Items were randomly selected from a large inventory. If 10% of the items in the inventory are made in Asia,

1. What is the probability that exactly 4 of the 20 items selected are made in Asia? (2 Points)

2. What is the probability that at most 4 of the 20 items selected are made in Asia? (2 Points)

Answer 1

Solution :

Let X be a random variable which represents the number of items in inventory which are made in Asia.

Also let's consider that "an item in inventory which is made in Asia" as success. So, now we have only two mutually exclusive outcomes (success and failure).

Given that 10% of the items in the inventory are made in Asia. Hence, probability of success is, p = 10/100 = 0.1

Number of trials (n) = 20

Now, since the probability of success remains constant in every trial, number of trials are finite and outcomes are independent to each other, therefore we can consider X as binomial distributed random variable.

According to binomial probability law, probability of occurrence of exactly x successes in n trials is given by,

1) We have to obtain P(X = 4).

We have, n = 20 and p = 0.1

Using binomial probability law we get,

Hence, the probability that exactly 4 of the 20 items selected are made in Asia is 0.0898.

2) We have to obtain P(X ≤ 4).

We have, n = 20 and p = 0.1

Using binomial probability law we get,

(Since, 0! = 1 and 1! = 1)

Hence, the probability that at most 4 of the 20 items selected are made in Asia is 0.9568.

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