The venn diagram below models probabilities of three events, a, b, and c.

By the conditional property we have:

If A and B are two events then A and B are independent if:

                               or

( since,

if two events A and B are independent then,

Now we know that:

Hence,

)

Based on the diagram that is given to us we observe that:

Region A covers two parts of the total area.

Hence, Area of Region A= 72/2=36

Hence, we have:

Also,

Region B covers two parts of the total area.

Hence, Area of Region B= 72/2=36

Hence, we have:

and A∩B covers one part of the total area.

i.e.

Area of A∩B=74/4=18

Hence, we have:

Hence, we have:

Hence, we have:

         Similarly we will have:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

rotation point l

step-by-step explanation: