Determine the probability $\mathrm{p}$, for each of the fonowing, (a) The sum of 6 appears in a single toss of a pair of fair dice.

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Determine the probability $\mathrm{p}$ , for each of the fonowing,
(a) The sum of 6 appears in a single toss of a pair of fair dice.

CBSE | Class 11 | Maths | NCERT Exemplar | Probability

Determine the probability $\mathrm{p}$ , for each of the fonowing,
(a) The sum of 6 appears in a single toss of a pair of fair dice.

Solution:

(a) When a pair of dice is rolled, total number of cases
$\begin{array}{l} S=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \\ (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \\ (4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\} \end{array}$
Total Sample Space, $n(S)=36$
Possible outcomes when sum is 6 are $(1,5),(2,4),(3,3),(4,2)$ and $(5,1)$ .
$\therefore$ Favourable no. of outcomes $=5$
It is known that,
$\begin{array}{l} \text { Probability }=\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }} \\ \therefore \text { Required probability }=\frac{5}{36} \end{array}$