3 A pair of dice is tossed once, find the probability of getting a) a total of 2 b) - Maths - Probability

Question

3 A pair of dice is tossed once, find the probability of
getting
a) a total of 2
b) a total of 5
c) an even number as the sum
d) same number on each dice

Manbar Singh · Accepted Answer

Let S be the sample space Now, Sample space is given by : $\begin{matrix} (1, 1), & (1, 2), & (1, 3), & (1, 4), & (1, 5), & (1, 6) \\ (2, 1), & (2, 2), & (2, 3), & (2, 4), & (2, 5), & (2, 6) \\ (3, 1), & (3, 2), & (3, 3), & (3, 4), & (3, 5), & (3, 6) \\ (4, 1), & (4, 2), & (4, 3), & (4, 4), & (4, 5), & (4, 6) \\ (5, 1), & (5, 2), & (5, 3), & (5, 4), & (5, 5), & (5, 6) \\ (6, 1), & (6, 2), & (6, 3), & (6, 4), & (6, 5), & (6, 6) \end{matrix}$ Now, nS = 36a Let E be the event of getting a sum of 2 Now, E =1,1nE = 1Now,pE = nEnS = 136b Let F be the event of getting a sum of 5 F = 1,4;2,3;3,24,1nF = 4Now, pF = nFnS = 436 = 19c Let G be the event of getting an even number as the sum Now, G = 1,1;1,3;1,5;2,2;2,4;2,6;3,1;3,3;3,5;4,2;4,4;4,6;5,1;5,3;5,5;6,2;6,4;6,6nG = 18So, pG = nGnS = 1836 = 12d Let H be the event of getting a same number on both dice H = 1,1;2,2;3,3;4,4;5,5;6,6nH = 6So, pH = nHnS = 636 = 16

3. A pair of dice is tossed once, find the probability of gettinga) a total of 2b) a total of 5c) an even number as the sumd) same number on each dice