Question

involving the green and red 10-sided dice.

What is the probability that both dice show an even number?

What is the probability that the product of the numbers rolled is less than 11?

Answer 1

(a)

10 - sided dice

Both dice show an even number

Favorable events:
S ={(2,2), (2,4), (2,6), (2,8),(2,10), (4,2), (4,4), (4,6), (4,8), (4,10), (6,2), (6,4), (6,6), (6,8), (6,10), (8,2), (8,4) (8,6), (8,8), (8,10), (10,2), (10,4), (10,6), (10,8), (10,10)} : 25 Nos.

So,

Probability that both dice show an even number = 25/100 = 0.25

So,

Answer is:

0.25

(b)

Product of th numbers rolled is less than 11:

Favorable Events :

S = {(1,1), (1,2), (1,3(, (1,4), (1,5), (1,6), (1,7),(1,8), (1,9), (1,10) : 10 Nos.

        (2,1), (2,2), (2,3), (2,4), (2,5) : 5 Nos.

       (3,1), (3,2), (3,3): 3 Nos.

       (4,1), (4,2): 2 Nos.

       (5,1), (5,2): 2 Nos.

       (6,1): 1 No.

         (7,1): 1 No.

         (8,1): 1 No.

         (9,1): 1 No.

          (10,1): 1 No. }

Thus, Number of favorable events = 27

So,

Probabilty that the product of the numbers rolled is less than 11 = 27/100 = 0.27

So,

Answer is:

0.27