a sociology teacher asked his students to com...
a sociology teacher asked his students to complete a survey at the beginning of the year. one survey question asked, \do you consider yourself responsible?\ another question asked, \how many siblings do you have?\ 0 siblings 1 or more siblings irresponsible 4 3 responsible 4 7 what is the probability that a randomly selected student has 1 or more siblings given that the student is irresponsible? simplify any fractions.
Answer
# Explanation:
## Step1: Recall conditional - probability formula
The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of frequency, if $A$ is the event of having 1 or more siblings and $B$ is the event of being irresponsible, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.
## Step2: Identify $n(A\cap B)$ and $n(B)$ from the table
From the table, the number of irresponsible students with 1 or more siblings $n(A\cap B) = 3$. The number of irresponsible students $n(B)=4 + 3=7$.
## Step3: Calculate the probability
$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{3}{7}$
# Answer:
$\frac{3}{7}$