Question

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

	a	b	c	total
female	9	3	12	24
total	28	7	18	53

round probabilities to 4 decimal places.
if one student is chosen at random,
find the probability that the student was male: 0.5472
find the probability that the student was male and got a \a\:
find the probability that the student was female or got an \a\:

Explanation:

Step1: Recall probability formula

$P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in event $E$ and $n(S)$ is the number of elements in the sample - space. Here, $n(S) = 53$.

Step2: Calculate probability of male and 'A'

The number of male students who got an 'A' is 19. So $P(\text{Male and A})=\frac{19}{53}\approx0.3585$.

Step3: Calculate probability of female or 'A'

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. The number of female students $n(\text{Female}) = 24$, the number of students who got an 'A' $n(\text{A}) = 28$, and the number of female students who got an 'A' $n(\text{Female and A}) = 9$.
$P(\text{Female})=\frac{24}{53}$, $P(\text{A})=\frac{28}{53}$, $P(\text{Female and A})=\frac{9}{53}$.
$P(\text{Female or A})=\frac{24 + 28-9}{53}=\frac{43}{53}\approx0.8113$.

Answer:

Find the probability that the student was male AND got a "A": 0.3585
Find the probability that the student was female OR got an "A": 0.8113