Chapter 13.6, Problem 2GP

To determine

To calculate: To find the probability of getting a even on dice and either heads or tails on coin

Answer to Problem 2GP

  $P\left(even,HeadsorTails\right)=\frac{1}{2}$

Explanation of Solution

Given information: A die is rolled and a coin is tossed

Formula Used:

Probability is defined as the likelihood of an event.

Probability is calculated as

  $\mathrm{Probability}=\frac{Event}{Outcomes}$

Calculation:

Event is defined as rolling a dice and tossing a coin simultaneously

Total number of possible outcomes $=6\times 2=12$

Now, getting a even on dice and either heads or tails on coin Possible outcomes are:

  $\begin{array}{l}\left(2,H\right),\left(2,T\right)\\ \left(4,H\right),\left(4,T\right)\\ \left(6,H\right),\left(6,T\right)\end{array}$

So, number of possible outcomes $=6$

Thus, probability is calculated as

  $\begin{array}{l}P\left(even,HeadsorTails\right)=\frac{6}{12}\\ P\left(even,HeadsorTails\right)=\frac{1}{2}\end{array}$

Conclusion:

Hence, the required probability is $\frac{1}{2}$