C3 Week 1 Summative Quiz: Q1 (Soccer and Basketball question)

Can someone please explain the solution please.

My Soln:
P(soccer) = 30/200
P(Basketball) = 100/200
P(Soccer and Basketball) = 70/200

P(Basketball | Soccer) = P( S and B) / P(S) = 7/3

But there is no option like that.
Please correct me if I am making any mistake

Hey @Sudeep53,
Welcome, and we are glad that you could become a part of our community :partying_face:

Please note the following statements:

30 of them like only soccer
100 of them like only basketball

Let me pose you a question, and perhaps it will help you understand the difference. As per you, P(Soccer) = 30/200, i.e., if you have a group of 200 people, and someone asks you just the following:

How many of these play soccer (these play may or may not play basketball)?

Your most likely estimate will be 30. However, if you take a look at the given information, do you think your estimate is correct?

In other words, would it be correct to translate “30 of them like only soccer” to “P(soccer) = 30 / 200”? If not, in what cases would it be incorrect? If yes, in what cases would it be correct.

Give this a thought, and I am sure you will move one step further in the direction of the correct answer.

P.S. - Probability can never be greater than 1 or smaller than 0. So whenever you arrive at a probability value violating either of these conditions, you can know for sure, that you have done a mistake.


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