The probability that it will take 5 or more flips of a fair coin before it lands on heads can be written as ab, where a and b are coprime positive integers. Find a+b.

To find the probability that it will take 5 or more flips of a fair coin before it lands on heads, we can consider the probability of getting tails on the first 4 flips and then getting heads on the fifth flip.

Since each flip of a fair coin is independent and has a 1/2 probability of landing on heads and 1/2 probability of landing on tails, the probability of getting tails on the first 4 flips is (1/2)^4.

The probability of getting heads on the fifth flip is also 1/2.

Therefore, the probability that it will take 5 or more flips before landing on heads is (1/2)^4 * (1/2) = 1/2^5 = 1/32.

Now, let's write this probability as a fraction in the form ab, where a and b are coprime positive integers.

1/32 is already in the desired form, with a = 1 and b = 32.

So, a + b = 1 + 32 = 33.

Therefore, the value of a + b is 33.