Question

A coin is tossed and a six sided die numbered 1 through 6 is rolled. Find the probability of tossing a head and then rolling a number greater then 4. Round to three decimal places

Answer 1

$\begin{gathered} \text{The sample space for a coin is 2} \\ S=(H,T) \\ \text{Thus, probability of tossing a head is:} \\ Pr(H)=\frac{1}{2} \end{gathered}$$\begin{gathered} \text{The sample space for a die is 6} \\ S=(1,2,3,4,5,6) \\ \text{Thus, the probability of rolling a number greater than 4 is:} \\ Pr(>4)=\frac{2}{6}=\frac{1}{3} \end{gathered}$

Hence, the probability of tossing a head and then rolling a number greater that 4 is:

$\begin{gathered} \frac{1}{2}\times\frac{1}{3} \\ \Rightarrow\frac{1}{6} \\ \Rightarrow0.167 \end{gathered}$