in a class of 26 students, 5 are female and 12 have an a in the class. there are 3 students who are female…

in a class of 26 students, 5 are female and 12 have an a in the class. there are 3 students who are female and have an a in the class. what is the probability that a student who has an a is a female?

in a class of 26 students, 5 are female and 12 have an a in the class. there are 3 students who are female and have an a in the class. what is the probability that a student who has an a is a female?

Answer

Explanation:

Step1: Identify relevant numbers

Let $A$ be the event of having an A and $F$ be the event of being female. We know $n(A) = 12$ (number of students with an A), $n(F\cap A)=3$ (number of female students with an A).

Step2: Use conditional - probability formula

The formula for conditional probability is $P(F|A)=\frac{P(F\cap A)}{P(A)}$. In terms of counts, $P(F|A)=\frac{n(F\cap A)}{n(A)}$. Substitute $n(F\cap A) = 3$ and $n(A)=12$ into the formula: $\frac{3}{12}$.

Step3: Simplify the fraction

$\frac{3}{12}=\frac{1}{4}=0.25$.

Answer:

$0.25$