NMIMS Decision Science Assignment Solution for September 2023

Q 1: Determine the probabilities for the below given statements and write your interpretation using following data.

		Do you like Anupama?
		NO	YES	TOTAL
Do you like “Kyuki Sas bhi kabhi bahu thi”?	NO	15	5	20
	YES	5	25	30
	TOTAL	20	30	50

1. What is the probability that randomly selected person has said “yes, I like Kyuki…”?
2. What is the probability that randomly selected person has said “ I don’t like Kyuki…”?
3. What is the probability that randomly selected person has said “yes, I like Anupama…”?
4. What is the probability that randomly selected person has said “ I don’t like Arupama…”?
5. What is the probability that randomly selected person has said ‘like Anupama’, also said
   ‘like kyuki….’ prior to that?
6. What is the probability that randomly selected person has said ‘like Kyuki….’, also said
   “don’t like Anupama” prior to that?
   Note: Do not use any software for the calculation, you are advised to show all necessary steps of
   calculations.

SOLUTION:

To calculate the probabilities and interpret the given data, let’s use the following notations:

• P(Kyuki) represents the event of liking “Kyuki sas bhi kabhi bahu thi.”
• P(Anupama) represents the event of liking “Anupama.”

1. Probability of saying “yes, I like Kyuki”: P(Kyuki, Yes) = 25/50 = 0.5 The probability that a randomly selected person says “yes, I like Kyuki” is 0.5 or 50%.
2. Probability of saying “I don’t like Kyuki”: P(Kyuki, No) = 5/50 = 0.1 The probability that a randomly selected person says “I don’t like Kyuki” is 0.1 or 10%.
3. Probability of saying “yes, I like Anupama”: P(Anupama, Yes) = 20/50 = 0.4 The probability that a randomly selected person says “yes, I like Anupama” is 0.4 or 40%.
4. Probability of saying “I don’t like Anupama”: P(Anupama, No) = (Total – P(Anupama, Yes)) = 1 – 0.4 = 0.6 The probability that a randomly selected person says “I don’t like Anupama” is 0.6 or 60%.
5. Probability of saying “like Anupama” and “like Kyuki”: P(Anupama, Yes, Kyuki, Yes) = P(Anupama, Yes) * P(Kyuki, Yes) = 0.4 * 0.5 = 0.2 The probability that a randomly selected person says “like Anupama” and “like Kyuki” is 0.2 or 20%.
6. Probability of saying “like Kyuki” and “don’t like Anupama”: P(Kyuki, Yes, Anupama, No) = P(Kyuki, Yes) * P(Anupama, No) = 0.5 * 0.6 = 0.3 The probability that a randomly selected person says “like Kyuki” and “don’t like Anupama” is 0.3 or 30%.

Interpretation:

1. There is a 50% probability that a randomly selected person likes “Kyuki sas bhi kabhi bahu thi.”
2. There is a 10% probability that a randomly selected person doesn’t like “Kyuki sas bhi kabhi bahu thi.”
3. There is a 40% probability that a randomly selected person likes “Anupama.”
4. There is a 60% probability that a randomly selected person doesn’t like “Anupama.”
5. There is a 20% probability that a randomly selected person likes both “Anupama” and “Kyuki sas bhi kabhi bahu thi.”
6. There is a 30% probability that a randomly selected person likes “Kyuki sas bhi kabhi bahu thi” but doesn’t like “Anupama.”

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