Question

What Numbers Go Into The Venn Diagram

Answer 1

Answer:

(a)The total number of outcomes where the sum is 9 or

    greater than 9 is  10

(b)Total number of outcomes where the sum is odd = 18

(c)Total number of outcomes where the  sum greater or equal to 9 and is

     also odd = 6

Step-by-step explanation:

Here, Sample Space = { Sum of the two digits when two dices are thrown together}

or,   S   =   {2,3,4,5,6,7,8,9,10,11,12}

(a)  The number of ordered pairs where sum is  9 or greater than 9

    = { sum is 9  ,  Sum is 10 ,  Sum is 11,   Sum is 12}

    = {(6,3)(3,6),(4,5)(5,4) ,   (5,5), (6,4),(4,6)  , (6,5)(5,6),   (6,6)}

Hence the total number of outcomes where the sum is 9 or

greater than 9 is  10

(b)  The number of ordered pairs where sum is odd.

    = { Sum is 3 ,  Sum is 5,   Sum is 7, Sum is 9, Sum is 11}

    = {(1,2)(2,1),   (4,1)(1,4),(2,3)(3,2) ,   (6,1), (1,6),(5,2),(2,5),(4,3)(3,4)  ,

        (6,3)(3,6), (4,5)(5,4),  (6,5),(5,6)}  = 18

Hence total number of outcomes where the sum is odd = 18

(c) Intersection point refers the outcomes which have sum greater or equal to 9 and is odd

Here, the possible outcomes are  = { Sum is 9 ,  Sum is 11}

                                            ={ (6,3)(3,6), (4,5)(5,4),  (6,5),(5,6)}  = 6

Hence total number of outcomes where the  sum greater or equal to 9 and is also odd = 6