Question

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

	a	b	c	total
female	18	2	3	23
total	29	18	7	54

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

Explanation:

Step1: Calculate probability of getting a B

The number of students who got a B is 18, and the total number of students is 54. The probability formula is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(\text{B})=\frac{18}{54}$.

Step2: Calculate probability of female and B

The number of female students who got a B is 2, and the total number of students is 54. So $P(\text{Female and B})=\frac{2}{54}$.

Step3: Calculate probability of male or B

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $P(\text{Male})=\frac{31}{54}$, $P(\text{B})=\frac{18}{54}$, and $P(\text{Male and B})=\frac{16}{54}$. Then $P(\text{Male or B})=\frac{31 + 18- 16}{54}$.

Answer:

$P(\text{B})=\frac{18}{54}\approx0.3333$
$P(\text{Female and B})=\frac{2}{54}\approx0.0370$
$P(\text{Male or B})=\frac{31 + 18- 16}{54}=\frac{33}{54}\approx0.6111$