Two fair dice are tossed together once. (a) Draw a sample space for the possible outcomes ; (b) Find the probability of getting a total : (i) of 7 or 8 ; (i...

Answer Details

(a) Sample space

Let the first number in each ordered pair be the score on the first die and the second number be the score on the second die.

Hence, there are \(6\times6=36\) equally likely outcomes.

(b)(i) Probability of a total of 7 or 8

A total of \(7\) occurs in 6 outcomes:

\((1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\).

A total of \(8\) occurs in 5 outcomes:

\((2,6),(3,5),(4,4),(5,3),(6,2)\).

Therefore,

\[P(7\text{ or }8)=\frac{6+5}{36}=\frac{11}{36}.\]

(b)(ii) Probability of a total less than 4

The possible totals are \(2\) and \(3\), obtained from:

\((1,1),(1,2),(2,1)\).

Thus,

\[P(\text{total less than }4)=\frac{3}{36}=\frac{1}{12}.\]