Answer :
Given
You flip a coin 3 times and roll a six sided die. Find the probability of getting 3 tails and rolling at least 4. Write answer as a reduced fraction.
Solution
Step 1
[tex]\begin{gathered} \text{Sample space for 3times flipping a coin} \\ HT,\text{ HT,HT} \\ ProbabilityG\text{etting a tail at one flip =}\frac{1}{2} \\ \therefore\text{Probability of getting 3 tails for 3times flipping=}\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} \text{Sample space of a sided die=1,2,3,4,5,6} \\ At\text{ least 4 means 4,5,6} \\ \text{Probability of getting at 4=}\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]Step 3
[tex]\text{Probability of gettings 3tails and rolling at 4=}\frac{1}{8}\times\frac{1}{2}=\frac{1}{16}[/tex]The final answer
[tex]\frac{1}{16}[/tex]