Question

the two dice are rolled simultaneously then fine probability is the the product of the digits on the upper surface is 12​

Answer 1

Answer:

S={(3,4),(4,3),(2,6),(6,2)}

Answer 2

The probability is $\frac{1}{9}$.

Step-by-step explanation:

The two dice are rolled.

Sample space = S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1),(5,2),(5,3), (5,4),(5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

So, n(S) = 36

E = the product of the digits on the upper surface is 12

E = {((2,6), (3,4), (4,3), (6,2)}

So, n(E) = 4

Now, probability = $\frac{n(E)}{n(S)}$

Probability = $\frac{4}{36} = \frac{1}{9}$

Hence, the probability is $\frac{1}{9}$