Question

Short answer

The probability of obtaining 4 is (a) \(\frac{1}{{12}}\), and of obtaining 10 is (b) \(\frac{1}{{12}}\).

Step-by-step solution

Given data

The total number of dice is \(n = 2\).

Understanding probability

The probability can be obtained by dividing the number of desired results by the number of possible results.

Evaluation of probability of obtaining 4 when you throw two dice  

The total number of possible results is 36 when you throw two dice.

The following are the possibility of coming 4.

\(\left( {1,3} \right),\left( {2,2} \right),\left( {3,1} \right)\)

The probability of getting 4 is calculated below:

\(\begin{array}{l}P = \frac{3}{{36}}\\P = \frac{1}{{12}}\end{array}\)

Thus, \(\frac{1}{{12}}\) is the required probability.

Evaluation of probability of obtaining 10 when you throw two dice  

The following are the possibility of coming 10.

\(\left( {4,6} \right),\left( {6,4} \right),\left( {5,5} \right)\)

The probability of getting 4 is calculated below:

\(\begin{array}{l}P = \frac{3}{{36}}\\P = \frac{1}{{12}}\end{array}\)

Thus, \(\frac{1}{{12}}\) is the required probability.