Question

what is the probability of those who are wearing brown shirts are male? (this is the conditional probability)

	brown	blue	green	total
female	40	40	10	90
total	90	80	30	200

a 45%
b 25%
c 56%
d 80%

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 the table, we want to find the probability that a person is male given they are wearing a brown shirt. Let $A$ be the event of being male and $B$ be the event of wearing a brown shirt. Then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of males wearing brown shirts and $n(B)$ is the total number of people wearing brown shirts.

Step2: Identify values from the table

From the table, $n(A\cap B) = 50$ (number of males wearing brown shirts) and $n(B)=90$ (total number of people wearing brown shirts).

Step3: Calculate the probability

$P=\frac{50}{90}=\frac{5}{9}\approx 0.56$ or $56\%$.

Answer:

C. 56%