Question

giving a test to a group of students, the grades and gender are summarized below

	a	b	c	total
female	16	10	6	32
total	25	14	8	47

if one student is chosen at random,
find the probability that the student got a c given they are female. give your answer as a decimal (to at least 4 places) or fraction

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, let $A$ be the event that a student got a 'C' and $B$ be the event that a student is female. Then $P(A|B)=\frac{\text{Number of female students with a C}}{\text{Total number of female students}}$.

Step2: Identify relevant values from the table

The number of female students who got a 'C' is 6, and the total number of female students is 32.

Step3: Calculate the probability

$P=\frac{6}{32}=\frac{3}{16}= 0.1875$

Answer:

$0.1875$