two dice are thrown at once. find the probability of getting multiple of 3 on one dice and multiple of 2 on the other.

Multiples of 3 in rolling a die is 3,6

 

Therefore,The probability of getting multiple of 3 is

Multiples of 2 in rolling a die is 2,4,6

 

Therefore, The probability of getting multiple of 2 is

Getting a multiple of 3 on one die is independent of getting a multiple of 2 on other die.

 

Let the events be A and B respectively.

 

Thus, the probability of getting multiple of 3 on one die and multiple of 2 on other die is

 

since A and B are independent events.

Thus,