Question

In the United States, 51% of all children get an allowance and 34% of all children get an allowance and do household chores. What is the probability that a child does household chores given that the child gets an allowance?33.33%66.67%50%100%

Answer 1

The conditional probability of event B happening given that event A happened is given by:

$P(B\vert A)=\frac{P(A\cap B)}{P(A)}$

Let A be the event "children get allowance and let B be the event "children do houshold chores". From the information given we have that:

$P(A)=.51$

and

$P(A\cap B)=.34$

Then the probability that a child does household chores given that it gets allowance is:

$\begin{gathered} P(B\vert A)=\frac{.34}{.51} \\ =0.6667 \end{gathered}$

Therefore the probability 66.67%