Answer:
Option D - 0.83
Step-by-step explanation:
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 ,
[tex]P(p)= 20\%=0.2\\P(c)= 80\%=0.8\\P(p\cap f)= 8\%=0.08\\P(c \cap f)= 66\%=0.66\\[/tex]
We have to find conditional probability where yoga student is female , given that the person studies yoga with Carl i.e, [tex]P(f/c)[/tex]
The formula is [tex]P(f/c)=\frac{P(f\cap c)}{P(c)}[/tex]
Substitute the values we get,
[tex]P(f/c)=\frac{0.66}{0.8}[/tex]
[tex]P(f/c)=0.825[/tex]
Approximately, [tex]P(f/c)=0.83[/tex]
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%.
