Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd}
B: {Sum of the numbers showing is 9,11, or 12}
Are events A and B independent? Why?

A and B are not independent.

Step-by-step explanation:

Two events are said to be independent if :

A: {Sum of the numbers showing is odd}

B: {Sum of the numbers showing is 9,11, or 12}

Given two dice, the sample space is given as:

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

The outcomes of event A:{Sum of the numbers showing is odd}  are:

(2,1),  (4,1), (6,1) ,  (1,2), (3,2),(5,2), (2,3), (4,3), (6,3)

(1,4), (3,4),  (5,4),  (2,5),  (4,5),  (6,5) , (1,6), (3,6),  (5,6)

P(A)=18/36

The outcomes of event B:{Sum of the numbers showing is 9,11, or 12} are:

(6,3) , (5,4),(4,5) (6,5) , (3,6), (5,6), (6,6)

P(B)=7/36

The intersection of A and B are:

(6,3) , (5,4),(4,5) (6,5) , (3,6), (5,6)

We can see from the above that:

Therefore, events A and B are not independent.

ans789

step-by-step explanation:

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.