Question

Let'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 8 total flips or fewer?

Answer 1

The probability of winning the game in 8 total flips or fewer is approximately 2.34%.

Step-by-step explanation:

To find the probability of winning the game in 8 total flips or fewer, we need to consider all possible outcomes that satisfy this condition.

There are 2 possible outcomes for each flip of the coin (Heads or Tails), so the total number of outcomes for 8 flips is 2^8 = 256.

To win the game, you must land on Heads 3 times in a row. This can happen in 6 different ways: HHH, THH, HTH, HHT, TTH, and HTT.

Therefore, the probability of winning in 8 total flips or fewer is 6/256 = 0.0234375, or approximately 2.34%.