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A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than 4 times? Express your answer as a common fraction.

 Aug 9, 2024
 #1
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The easiest way to solve this problem is with complementary counting.

There are 2 ways for the coin to be tossed less than or equal to 4 times:

1. 3 in a row for heads

There is a (1/2)^3 probability for this to happen in 3 tosses and a (1/2)^4 chance for it to happen in 4.

2. 3 in a row for tails

This is the same as case 1, just with heads and tails reversed.

 

Adding up all the ways, it is 2(1/8+1/16) or 3/8 chance for the coin to be tossed less than or equal to 4 times.

Subtracting it from 1 gives 5/8, the odds for the coin to be tossed more than 4 times.

 Aug 10, 2024

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