Question

Drag the tiles to the correct boxes to complete the pairs. Suppose you roll a fair six-sided die. Then you roll a fair eight-sided die. Match each probability to its correct value. the probability that both numbers are odd numbers and their product is greater than 10 the probability that the second number is twice the first number the probability of getting numbers whose sum is a multiple of 4 the probability that the sum of the two numbers is greater than 11 the probability that the second number rolled is less than the first number arrowRight arrowRight arrowRight arrowRight arrowRight

1. The probability will be:
Case 1  matches with 5/48.
Case 2 matches with 1/12.
Case 3 matches with 1/4.
Case 4 matches with 1/8.
Case 5 matches with 5/16.

### How to illustrate the probability?

We have a total sample space of six-sided die and an eight  sided die.
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)
Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are:  (3,5),(3,7),(5,3),(5,5),(5,7)
And the total number of outcomes are: 48.
The required probability is 5/48.
Case 2: The probability that the second number is twice the first number are:
(1,2),(2,4),(3,6),(4,8)
And the total number of outcomes are 48.
So, the required probability is 1/12.
Case 3: The probability of a number whose sum is a multiple of 4 are:
(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).
And the total number of outcomes are: 48.
The required probability is 12/48 = 1/4
Case 4: The probability that the sum of two numbers is greater than 11.
(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)
And a total number of outcomes are 48.
So, the required probability is 6/48 = 1/8.
Case 5: The probability that the second number rolled is less than the first number are:
(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)
And the total number of outcomes are: 48.
The required probability is 15/48 = 5/16.