Question

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

	a	b	c	total
female	7	5	15	27
total	19	23	17	59

if one student is chosen at random, find the probability that the student was male or got an \a\. type as a fraction.

Explanation:

Step1: Use the formula for $P(A\cup B)$

$P(\text{Male}\cup\text{"A"})=P(\text{Male}) + P(\text{"A"})-P(\text{Male and "A"})$

Step2: Calculate $P(\text{Male})$

The number of male students is 32 and the total number of students is 59. So $P(\text{Male})=\frac{32}{59}$

Step3: Calculate $P(\text{"A"})$

The number of students who got an "A" is 19. So $P(\text{"A"})=\frac{19}{59}$

Step4: Calculate $P(\text{Male and "A"})$

The number of male students who got an "A" is 12. So $P(\text{Male and "A"})=\frac{12}{59}$

Step5: Substitute values into the formula

$P(\text{Male}\cup\text{"A"})=\frac{32}{59}+\frac{19}{59}-\frac{12}{59}=\frac{32 + 19- 12}{59}=\frac{39}{59}$

Answer:

$\frac{39}{59}$