Question

chapter 4.3 homework
score: 29/42 answered: 24/33
question 25
0/1 pt 2 99 details
4.3 conditional probability. two - way conditional table.
giving a test to a group of students, the grades and gender are summarized below

	a	b	c	total
female	7	18	5	30
total	13	29	22	64

if one student is chosen at random, find the probability that the student was female or got an \c\. type as a fraction.
question help: video message instructor

Explanation:

Step1: Recall probability formula

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that the student is female and $B$ be the event that the student got a 'C'.

Step2: Calculate $P(A)$

The number of female students is $30$, and the total number of students is $64$. So $P(A)=\frac{30}{64}$.

Step3: Calculate $P(B)$

The number of students who got a 'C' is $22$, so $P(B)=\frac{22}{64}$.

Step4: Calculate $P(A\cap B)$

The number of female students who got a 'C' is $5$, so $P(A\cap B)=\frac{5}{64}$.

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{30}{64}+\frac{22}{64}-\frac{5}{64}=\frac{30 + 22- 5}{64}=\frac{47}{64}$.

Answer:

$\frac{47}{64}$