Two dice with faces 1, 2, 3, 4, 5 ,6 are thrown and the sum if the faces is counted. Plot the probability mass function for the sum of the faces. What is the probability that the product of the faces is 12?

Mumbai University > Electronics and Telecommunication > Sem5 > Random Signal Analysis

Marks: 10M

Year: Dec 2014

When 2 fair dice are thrown, the sample space is given by

$S= $$ \begin{Bmatrix} \ (1,1) & (1,2) & (1,3)&(1,4)&(1,5)&(1,6) \\ \ (2,1) & (2,2) & (2,3)&(2,4)& (2,5)&(2,6)\\ (3,1) & (3,2) & (3,3) &(3,4)&(3,5)&(3,6) \\ \ (4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6) \\ \ (5,1) &(5,2)& (5,3)&(5,4)&(5,5)&(5,6) \\ \ (6,1) &(6,2)&(6,3)&(6,4)&(6,5)&(6,6) \\ \end{Bmatrix} $ $$n(S)=36$$ Probability mass function (pmf) for the sum of the faces is given by ![enter image description here][1] Cumulative distribution function (cdf) for the sum of the faces is given by ![enter image description here][2] Let ‘A’ be the event that the product of the faces is 12 A={(2,6),(3,4),(4,3),(6,2)} n(A)=4 $$∴P(A)=n(A)/n(S) =4/36=1/9$$

∴ The probability that the product of the faces is 12 = 1/9