Question

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.

Answer 1

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

`\begin{gathered} \text{Sample space for 3times flipping a coin} \\ HT,\text{ HT,HT} \\ ProbabilityG\text{etting a tail at one flip =}(1)/(2) \\ \therefore\text{Probability of getting 3 tails for 3times flipping=}(1)/(2)*(1)/(2)*(1)/(2)=(1)/(8) \end{gathered}`

Step 2

`\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=}(3)/(6)=(1)/(2) \end{gathered}`

Step 3

`\text{Probability of gettings 3tails and rolling at 4=}(1)/(8)*(1)/(2)=(1)/(16)`

The final answer

`(1)/(16)`