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.35
B.56
C.69
D.83

Given : 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.

To find : What is the probability that a randomly selected yoga student is female, given that the person studies yoga with Carl?

Solution :

Let p- Patrick , c-Carl and f-female

So, we have given that ,

\(P(p)= 20\%=0.2\\P(c)= 80\%=0.8\\P(p\cap f)= 8\%=0.08\\P(c \cap f)= 66\%=0.66\\\)

We have to find conditional probability where yoga student is female , given that the person studies yoga with Carl i.e, \(P(f/c)\)

The formula is \(P(f/c)=\frac{P(f\cap c)}{P(c)}\)

Substitute the values we get,

\(P(f/c)=\frac{0.66}{0.8}\)

\(P(f/c)=0.825\)

Approximately, \(P(f/c)=0.83\)

Therefore, 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%.

theman453123 theman453123 · Answer 2 · 2021-04-12T17:23:53-04:00

theman453123 theman453123

12-04-2021

Answer:

0.83

Please give me brainliest, I really need it.

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