question_answer

Two dice are thrown simultaneously. The probability of getting a multiple of 2 on one die and a multiple of 3 on the other is ____.

A) \[\frac{5}{36}\]                         

B) \[\frac{5}{12}\]             

C)  \[\frac{11}{36}\]                                  

D)  \[\frac{1}{12}\]            

Correct Answer: C

Solution :

Let S be the sample space of throwing two dice then,

	(1, 1),	(1,2),	(1,3),	(1,4),	(1,5),	(1,6);
	(2,1),	(2,2),	(2,3),	(2,4),	(2,5),	(2,6);
S =	(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)

 Total number of outcomes = 36 Number of favorable outcomes = {(2, 3), (2, 6), (3, 2), (3, 4), (3, 6), (4, 3), (4, 6), (6, 2), (6, 3), (6, 4), (6, 6)} i.e., 11 in number  Required probability