Question

When two dice are tossed what is the probability that the total score is a composite number?

Answer 1

Total number of outcomes=6^2=36
Favourable outcomes =1-3,1-5,2-2,2-4,2-6,3-1,3-3,3-5,3-6,4-2,4-4,4-5,4-6,5-1,5-3,5-4,5-5,6-2,6-3,6-4,6-6
Favourable number of outcomes=21
P(composite number)=36/21=12/7

Answer 2

GIVEN,

Two dice are tossed.

TO FIND,

The probability that a total score is a composite number.

SOLUTION,

we know that a composite number is formed by multiplying two smaller integers,

the composite number we know from 1-12 ( because the dice is thrown twice 6+6) are 4,6,8,9,10 and 12.

now outcomes of total score as the composite number will be,

1-3, 3-1, 2-2, 2-4, 4-2,1-5, 5-1, 3-3, 6-2, 2-6, 5-3, 3-5, 4-4,

      ↓                             ↓                              ↓

      4                             6                              8

5-4, 4-5, 6-3, 3-6, 5-5, 6-4, 4-6, 6-6

       ↓                            ↓               ↓

       9                            10              1

hence total outcomes will be= 21.

total outcomes of throwing two dice= 36

hence P(favorable outcomes)= $\frac{21}{36}$

           P( total score as a composite number) = $\frac{7}{12}$

HENCE THE PROBABILITY OF THE TOTAL SCORE IS A COMPOSITE NUMBER IS $\frac{7}{12}$.