There is a jar full of 10 coins. 9 are fair, and 1 has both faces showing heads. you draw a coin at random from the jar and flip it 5 times. if you flip heads 5 times in a row, what is the probability that you get heads on your next flip?

step-by-step explanation:

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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