Question

Two dice are drawn simultaneously. A fraction a/b is formed such that a is the number shown on the first dice and b is the number shown on the second dice. What is the probability that the fraction a/b is greater than 1? ​

Answer 1

Answer:

5/12

Step-by-step explanation:

Two dice are drawn simultaneously. A fraction a/b is formed such that a is the number shown on the first dice and b is the number shown on the second dice. What is the probability that the fraction a/b is greater than 1? ​

a/b > 1

=> a > b

number shown on first dice > number shown on second dice

Dice has numbers from 1 to 6

so total possible combination

= 6 * 6 = 36

if second dice = 6 then first dice have no favorable possible to have greater value

if second dice = 5 then first dice = 6  - 1 favorable possible

if second dice = 4 then first dice = 5 or 6  - 2 favorable possible

if second dice = 3 then first dice = 4 , 5 or 6  - 3 favorable possible

if second dice = 2 then first dice = 3 , 4 , 5 or 6  - 4 favorable possible

if second dice = 1 then first dice = 2 , 3 , 4 , 5 or 6  - 5 favorable possible

so total favorable possibles = 1 + 2 + 3 + 4 + 5 = 15

Probability = Favorable / Total

hence Probability = 15/36 = 5/12

probability that the fraction a/b is greater than 1 = 5/12