96.4k views
5 votes
In Maharashtra there are 20 Big companies in IT sector. Out of these, 15 companies are in Mumbai. What is probability that at least two companies are from Mumbai if total 3 companies selected randomly to form a sample

User Rashkay
by
8.3k points

1 Answer

5 votes

see below

To calculate the probability that at least two companies are from Mumbai, we need to consider two separate scenarios:

Scenario 1: Exactly 2 companies are from Mumbai

* Choose 2 companies out of the 15 companies in Mumbai: C(15, 2)

* Choose 1 company out of the remaining 5 companies outside Mumbai: C(5, 1)

* Total number of ways to choose a sample of 3 companies: C(20, 3)

Scenario 2: All 3 companies are from Mumbai

* Choose 3 companies out of the 15 companies in Mumbai: C(15, 3)

* Total number of ways to choose a sample of 3 companies: C(20, 3)

The probability that at least two companies are from Mumbai is the sum of the probabilities from these two scenarios:

Probability = (C(15, 2) \* C(5, 1) + C(15, 3)) / C(20, 3)

Now, let's calculate the probability:

Probability = ((15! / (2! \* 13!)) \* (5! / (1! \* 4!)) + 15! / (3! \* 12!)) / (20! / (3! \* 17!))

Simplifying the expression:

Probability = (105 \* 5 + 455) / 1140

Probability = 560 / 1140

Probability ≈ 0.491

Therefore, the probability that at least two companies are from Mumbai, when selecting a random sample of 3 companies from the 20 big IT companies in Maharashtra, is approximately 0.491 or 49.1%.

User Chan Myae Thu
by
8.2k points