# If two balanced dice are rolled, what is the probability that the sum of the numbers that appear will be odd?

Probability = No. Of favorable ways / Total ways

where ,

Total ways  =  no. Of favorable ways + no. Of non-favorable  ways

Since,          odd no. + odd no. = even no.

even no. + even no. = even no.

odd no. + even no. = odd no.

according to question, sum of numbers is odd -

Hence,  one dice should show an even number like 2  or 4  or 6 an other dice should show an odd number 1  or 3  or 5.

making all pairs as --- ( no. On 1st dice ,  no. On second dice )

(1 , 2)    (2, 1)    (1 , 4)    (4, 1)    (1, 6)    (6, 1)

(3, 2)    (2, 3)  (3, 4)    (4, 3)  (3, 6)    (6,3)

(5, 2)    (2,5)    (5,4)      (4,5)    (5,6)    (6,5)

No. Of Favorable ways (pairs) = 6 + 6 + 6 = 18

Total ways  = ways of any no. Showing on dice 1 x ways of any                                    no. Showing on dice 2 = total no. Of Pairs

( when 2 process occur simultaneously independently then their no. Of ways are multiplied )

= 6 x 6 = 36

hence probability = Favorable ways / Total ways

= 18 / 36 = 1/2 = 0.5

thanked the writer.