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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