Question

Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

Answer 1

It is given that the two numbers are different that appears on throwing the two dices.

When two dices are thrown, then the total number of sample spaces is 36.

Let A be the event that the sum of the numbers on two dices is 4 and B be the event that the numbers appearing on throwing the two dices are different.

A={ ( 1,3 ),( 2,2 ),( 3,1 ) } P( A )= 3 36

And,

B={ ( 1,2 ),( 1,3 ),( 1,4 ),( 1,5 ),( 1,6 ) ( 2,1 ),( 2,3 ),( 2,4 ),( 2,5 ),( 2,6 ) ( 3,1 ),( 3,2 ),( 3,4 ),( 3,5 ),( 3,6 ) ( 4,1 ),( 4,2 ),( 4,3 ),( 4,5 ),( 4,6 ) ( 5,1 ),( 5,2 ),( 5,3 ),( 5,4 ),( 5,6 ) ( 6,1 ),( 6,2 ),( 6,3 ),( 6,4 ),( 6,5 ) } P( B )= 30 36 = 5 6

Now,

A∩B={ ( 1,3 ),( 3,1 ) } P( A∩B )= 2 36 = 1 18

The conditional probability P( A|B ) is calculated as,

P( A|B )= P( A∩B ) P( B ) = 1 18 5 6 = 1 15

Therefore, the probability is 1 15 .