+1427 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.
+10 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.
