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Answer :
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%.
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