SOLUTION: A coin is tossed continuously until either a head turns up or a total of three tails comes up.What is the expected number of tosses for this event?

Question 33820: A coin is tossed continuously until either a head turns up or a total of three tails comes up.What is the expected number of tosses for this event?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The head comes up either on the 1st toss, or the 2nd toss or on the 3rd
toss. If no head on 1,2, or 3 we have ttt so we are finished.
Take each case; count the number of tosses involved; multiply by the probability of this particular case. Then add up the products to get the
expected value.
Here we go:
h number of tosses=1 probability of this = 1/2; product = 1(1/2)= 1/2
th number of tosses=2 prob of this is 1/4; product is 2(1/4)= 1/2
tth number of tosses=3 prob of this is 1/8; product is 3(1/8)=3/8
ttt number of tosses=3 prob of this is 1/8; product is 3(1/8)=3/8
Expected value = 1/2 + 1/2 + 3/8 + 3/8= 14/8=7/4=1.75 tosses
Cheers,
Stan H.
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