Use the "at least once" rule to find the probabilities of the following events. getting at least one tail when tossing nine fair coins the probability is (type an integer or a simplified fraction.)

Step-by-step explanation:

We know that the total number of faces on a coin [Tail, Heads] =2

The probability of getting a tail =

The  probability of getting no tail =

The "at least once" rule says that the when a coin is tossed n times , then the probability of getting at least one tail is given by :-

Since , n=9

Then, the probability of getting at least one tail is given by :-

The probability is

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