in a class of students, the following data table summarizes how many students have a brother or a sister…

in a class of students, the following data table summarizes how many students have a brother or a sister. what is the probability that a student has a sister given that they do not have a brother?\n| |has a brother|does not have a brother|\n|--|--|--|\n|has a sister|8|12|\n|does not have a sister|5|4|

in a class of students, the following data table summarizes how many students have a brother or a sister. what is the probability that a student has a sister given that they do not have a brother?\n| |has a brother|does not have a brother|\n|--|--|--|\n|has a sister|8|12|\n|does not have a sister|5|4|

Answer

Answer:

$\frac{12}{16}$

Explanation:

Step1: Identify relevant values

We want $P(\text{has sister}|\text{no brother})$. The number of students with no brother and a sister is 12, and the number of students with no brother is $12 + 4=16$.

Step2: Apply conditional - probability formula

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, $P(\text{has sister}|\text{no brother})=\frac{\text{Number of students with no brother and sister}}{\text{Number of students with no brother}}=\frac{12}{16}$.