the central high school students voted to select a school mascot. the results of the vote are recorded in…

the central high school students voted to select a school mascot. the results of the vote are recorded in the table. a student is randomly selected. if the student voted for a falcon mascot, what is the probability that the student is a junior?\n| class | falcon | eagle | total |\n| ---- | ---- | ---- | ---- |\n| freshman | 155 | 90 | 245 |\n| sophomore | 160 | 65 | 225 |\n| junior | 100 | 130 | 230 |\n| senior | 165 | 55 | 220 |\n| total | 580 | 340 | 920 |\na $\frac{10}{23}$ b $\frac{5}{29}$ c $\frac{5}{46}$ d $\frac{10}{13}$

the central high school students voted to select a school mascot. the results of the vote are recorded in the table. a student is randomly selected. if the student voted for a falcon mascot, what is the probability that the student is a junior?\n| class | falcon | eagle | total |\n| ---- | ---- | ---- | ---- |\n| freshman | 155 | 90 | 245 |\n| sophomore | 160 | 65 | 225 |\n| junior | 100 | 130 | 230 |\n| senior | 165 | 55 | 220 |\n| total | 580 | 340 | 920 |\na $\frac{10}{23}$ b $\frac{5}{29}$ c $\frac{5}{46}$ d $\frac{10}{13}$

Answer

Explanation:

Step1: Identify relevant values

We want the probability that a student is a junior given they voted for a falcon. The number of juniors who voted for a falcon is 100, and the total number of students who voted for a falcon is 580.

Step2: Apply conditional - probability formula

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event that the student is a junior and $B$ is the event that the student voted for a falcon, the probability $P(A|B)=\frac{\text{Number of juniors who voted for falcon}}{\text{Total number of students who voted for falcon}}$. So $P=\frac{100}{580}=\frac{5}{29}$.

Answer:

B. $\frac{5}{29}$