Question

Of all the yoga students in a particular area, 20% study with patrick and 80% study with carl. we also know that 8% of the yoga students study with patrick and are female, while 66% of the students study with carl and are female. what is the probability that a randomly selected yoga student is female, given that the person studies yoga with carl? a. 0.35 b. 0.56 c. 0.69 d. 0.83

Answer 1

The option D is correct. The probability that a randomly selected yoga student is female, given that the person studies yoga with Carl is 0.83 or 83%.

According to the statement

we have given that the Of all the yoga students in a particular area, 20% study with Patrick and 80% study with Carl. We also know that 8% of the yoga students study with Patrick and are female, while 66% of the students study with Carl and are female.

And we have to find that the probability that a randomly selected yoga student is female, given that the person studies yoga with Carl.

So, For this purpose,

Let p- Patrick , c-Carl  and f-female

And we have given that the

P(p) = 20% = 0.2

P(c) = 80% = 0.8

P(p ∩ f) = 8% = 0.08

P(c ∩  f) = 66% = 0.66

Then

We have to find conditional probability where yoga student is female , given that the person studies yoga with Carl

It become according to conditional probability formula:

P(f/c) = P(c ∩  f) / P(c)

Substitute the values in it then

P(f/c) = 0.66 / 0.8

P(f/c) = 0.825

Approximately 0.83.

So, The option D is correct. The probability that a randomly selected yoga student is female, given that the person studies yoga with Carl is 0.83 or 83%.

Learn more about Conditional Probability here

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