Question

et's say are a playing a game in which you must flip a (fair) coin and land on heads 3 times in a row. what is the probability you will win in 6 total flips or fewer?

Answer 1

The probability of winning in 6 total flips or fewer is 15/64.

Step-by-step explanation:

To find the probability of winning in 6 total flips or fewer, we need to calculate the probability of getting 3 heads in a row in 6 flips or fewer.

To calculate this, we'll consider the possible ways to get 3 heads in a row in 6 flips or fewer:

1. Winning on the first 3 flips: probability = (1/2) * (1/2) * (1/2) = 1/8
2. Winning on the first 4 flips: probability = (1/2) * (1/2) * (1/2) * (1/2) = 1/16
3. Winning on the first 5 flips: probability = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
4. Winning on the first 6 flips: probability = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/64

So the total probability of winning in 6 flips or fewer is:

P(win in 6 flips or fewer) = 1/8 + 1/16 + 1/32 + 1/64 = 15/64