John has the phone numbers of many young ladies. Some of these young ladies are

Question

John has the phone numbers of many young ladies. Some of these young ladies are blonde and others are brunettes. In addition, John knows that some are single while others have boyfriends. The exact breakdown is as follows:

Blonde Brunette Single 15 12 Taken 10 18

Find the following probabilities:

Q10: What is the probability of selecting someone who is taken, given that they are blonde?

Q11: What is the probability of selecting a single brunette?

Q12: What is the probability of selecting someone who is brunette, given that they are taken?

Explanation / Answer

Here, we are given the frequency distribution as:

Q10) Given that the girl is blonde, probability that someone who is taken is computed as:

= Number of blonde girls who are taken / Number of blondes

= 10 / (25 )

= 0.4

Therefore 0.4 is the required probability here.

Q11) Probability of selecting a single brunette is computed as:

= Total number of brunette / Total number of girls in the sample

= ( 30) / (30 + 25 )

= 0.5455

Therefore 0.5455 is the required probability here.

Q12) Now the probability of selecting someone who is brunette, given that they are taken is computed as:

= Total number of brunette who are taken / Total number of taken girls

= 18 / (18 + 10 )

= 0.6429

Therefore 0.6429 is the required probability here.

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