If in a total of 15 days, Allie has 12 days with math homework, the probability of a given day having a math homework is:
[tex]P(m)=\frac{12}{15}[/tex]Similarly, for the science homework, we have that:
[tex]P(s)=\frac{9}{15}[/tex]In order to calculate the probability of a given day having both homeworks, we can calculate the product of these probabilities:
[tex]P(m\cap s)=P(m)\cdot P(s)=\frac{12}{15}\cdot\frac{9}{15}=\frac{4}{5}\cdot\frac{3}{5}=\frac{12}{25}=0.48=48\text{\%}[/tex]So the probability of having both homeworks in a given day is 48%.
