PLEASE HELP
Which of the following are true if event A and B are independent

a)

Step-by-step explanation:

Step(i):-

Given that A and B are independent events

P(A∩B) =P(A) P(B)

we will use the conditional probability

                     or

Step(ii):-

Given that A and B are independent events

P(A∩B) =P(A) P(B)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4