giving a test to a group of students, the grades and gender are summarized below\ngrades and gender\n| | a |…

giving a test to a group of students, the grades and gender are summarized below\ngrades and gender\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 14 | 19 | 5 | 38 |\n| female | 6 | 10 | 3 | 19 |\n| total | 20 | 29 | 8 | 57 |\nif one student is chosen at random, find the probability that the student was female or got an \b\. round your answer to 4 decimal places.

giving a test to a group of students, the grades and gender are summarized below\ngrades and gender\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 14 | 19 | 5 | 38 |\n| female | 6 | 10 | 3 | 19 |\n| total | 20 | 29 | 8 | 57 |\nif one student is chosen at random, find the probability that the student was female or got an \b\. round your answer to 4 decimal places.

Answer

Explanation:

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

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

Step2: Calculate $P(A)$

The number of female students is $19$, and the total number of students is $57$. So $P(A)=\frac{19}{57}$.

Step3: Calculate $P(B)$

The number of students who got a "B" is $29$, and the total number of students is $57$. So $P(B)=\frac{29}{57}$.

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

The number of female students who got a "B" is $10$, and the total number of students is $57$. So $P(A\cap B)=\frac{10}{57}$.

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

$P(A\cup B)=\frac{19}{57}+\frac{29}{57}-\frac{10}{57}=\frac{19 + 29- 10}{57}=\frac{38}{57}\approx0.6667$

Answer:

$0.6667$