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 In a group of 24 members, each member drinks either tea or coffee or both. If 15 of them drink tea and 18 drink coffee, find the probability that a person selected from the group drinks both tea and coffee.
1. 1 / 8
2. 3 / 8
3. 5 / 24
4. None of the options

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Correct Answer - Option 2 : 3 / 8

Answer: Option 2

Data

Probability of a member drinks Tea: P(Tea) =  \(\frac{{15}}{{24}}\)

Probability of a member drinks coffee: P(Coffee) = \(\frac{{18}}{{24}}\)

Probability of member either drinks tea or coffee : P(Tea ∪ Coffee) = \(\frac{{24}}{{24}}\) ≡ 1 ( given in the Question; that each member drinks either tea or coffee or both)

Calculation

Using set inclusion-Exclusion principle 

P(Tea ∪ Coffee) = P(Tea) + P(Coffee) - P(Tea ∩ Cofee)

1 = \(\frac{{15}}{{24}}\) + \(\frac{{18}}{{24}}\) - P(Tea ∩ Coffee)

P(Tea ∩ Coffee) = \(\frac{{15}}{{24}}\) + \(\frac{{18}}{{24}}\) - 1 

P(Tea ∩ Coffee) = \(\frac{{33-24}}{{24}}\)

P(Tea ∩ Coffee) = \(\frac{{9}}{{24}}\) ≡ \(\frac{{3}}{{8}}\)

Hence Option 2 is the correct answer

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