Question

chapter 3: 3.3 two basic rules of probability homework due: sun sep 14, 2025 11:59pm attempt 1 in progress next up: submit assignment details no additional details were added for this assignment. chapter 3: 3.3 two basic rules of probability homework score: 6/14 answered: 3/8 question 4 2 pts giving a test to a group of students, the grades and gender are summarized below grades and gender a b c total male 3 7 19 29 female 6 10 13 29 total 9 17 32 58 if one student is chosen at random, find the probability that the student was female or got an \a\. round your answer to 4 decimal places.

Explanation:

Step1: Recall the formula for the probability of the union of two events

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 an 'A'.

Step2: Calculate $P(A)$

The number of female students is $29$, and the total number of students is $58$. So $P(A)=\frac{29}{58}$.

Step3: Calculate $P(B)$

The number of students who got an 'A' is $9$, so $P(B)=\frac{9}{58}$.

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

The number of female students who got an 'A' is $6$, so $P(A\cap B)=\frac{6}{58}$.

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

$P(A\cup B)=\frac{29}{58}+\frac{9}{58}-\frac{6}{58}=\frac{29 + 9-6}{58}=\frac{32}{58}\approx0.5517$.

Answer:

$0.5517$