The probability of getting a sum 9 when two dice are thrown is

The probability of getting a sum 9 when two dice are thrown is
  1. $\frac{1}{6}$
  2. $\frac{1}{8}$
  3. $\frac{1}{9}$
  4. $\frac{1}{12}$

Solution

When two dice are rolled together, then total outcomes are 36 and sample space is $\begin{aligned} & {[(1,1),(1,2),(1,3),(1,4),(1,5)(1,6),} \\ & (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), \\ & (3,1),(3,2),(3,3),(3,4),(3,5),(3,6), \\ & (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), \\ & (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), \\ & (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]\end{aligned}$ So, pairs with sum 9 are $(3,6)(4,5),(5,4),(6,3)$ i.e total 4 pairs. Total outcomes $=36$ Favourable outcomes $=4$ Probability of getting the sum of 9 $=\frac{4}{36}=\frac{1}{9}$

Asked in: AP EAMCET 2022 (05 Jul Shift 1)

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