Suppose you roll a fair six sided die. then you roll a fair eight sided die. match each probability to it's correct value.

Case 1  matches with .

Case 2 matches with .

Case 3 matches with .

Case 4 matches with .

Case 5 matches with .

Step-by-step explanation:

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 total number of outcomes are: 48.

So, required probability is:.

Case 2: The probability that second number is twice the first number are:

(1,2),(2,4),(3,6),(4,8)

And total number of outcomes are: 48.

So, required probability is:.

Case 3: The probability of a number whose sum is 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 total number of outcomes are: 48.

So, required probability is:.

Case 4: The probability that sum of two numbers is greater than 11.

(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)

And total number of outcomes are: 48.

So, required probability is:.

Case 5:The probability that second number rolled is less than 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 total number of outcomes are: 48.

So, required probability is:.

So, the correct matches are:

Case 1  matches with .

Case 2 matches with .

Case 3 matches with .

Case 4 matches with .

Case 5 matches with .

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.