after giving a test to a group of students, the grades and gender are summarized below.\n| | a | b | c |…

after giving a test to a group of students, the grades and gender are summarized below.\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 11 | 16 | 4 | 31 |\n| female | 18 | 2 | 3 | 23 |\n| total | 29 | 18 | 7 | 54 |\nround probabilities to 4 decimal places.\nif one student is chosen at random,\nfind the probability that the student got a b:\nfind the probability that the student was female and got a \b\:\nfind the probability that the student was male or got an \b\:

after giving a test to a group of students, the grades and gender are summarized below.\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 11 | 16 | 4 | 31 |\n| female | 18 | 2 | 3 | 23 |\n| total | 29 | 18 | 7 | 54 |\nround probabilities to 4 decimal places.\nif one student is chosen at random,\nfind the probability that the student got a b:\nfind the probability that the student was female and got a \b\:\nfind the probability that the student was male or got an \b\:

Answer

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:

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