A mobile provider believes that its new promotion will convince 20% of their competitors' customers to switch to their own service. If the company's forecasts are correct, what is the approximate probability that one out of four randomly selected competitors' customers will switch after exposure to the promotion

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

=

x=0.8898305 is the answer to that equation