If you’re wondering about the odds of a coin flip resulting in the same outcome multiple times in a row, here’s how it works:
- Independent events: Each coin flip is considered an independent event. This means the outcome of one flip doesn’t affect the outcome of the next. The coin doesn’t have a memory, [according to Quora].
- Probability of a single event: For a fair coin, the probability of getting heads (H) is 1/2 or 50%. The probability of getting tails (T) is also 1/2 or 50%.
- Calculating successive probabilities: To find the probability of multiple independent events occurring in a specific sequence, you multiply the probabilities of each individual event.
- Two heads in a row: The probability is (1/2) * (1/2) = 1/4 = 25%.
- Three heads in a row: The probability is (1/2) (1/2) (1/2) = 1/8 = 12.5%.
- N heads in a row: The probability is (1/2) raised to the power of N, or (1/2)^N. For example, the probability of 10 heads in a row is 1/1024 or approximately 0.00098.
Important Note: Even if you’ve flipped heads many times in a row, the probability of getting heads on the next flip is still 50% (assuming a fair coin and fair flipping). This is a common misconception known as the Gambler’s Fallacy.
What are the odds of getting a streak on a coin flip?
Good point! So you have around a fifty percent chance of getting a streak of at least three heads if you flip a coin ten times. Pretty high chance, isn’t it? For at least four consecutive heads the probability falls to around 25%, for streaks of five heads or more it’s still around 10%, and then for six it’s a bit less than 5%.
What are the chances of winning a 50/50 3 times in a row?
Great question! Three flips of a fair coin
Suppose you have a fair coin: this means it has a 50% chance of landing heads up and a 50% chance of landing tails up. Suppose you flip it three times and these flips are independent. What is the probability that it lands heads up, then tails up, then heads up? So the answer is 1/8, or 12.5%.
How to calculate probability of consecutive coin flips?
And since it wants four times in a row we’re just going to have to do this four. Times. So 2 * 2 is 4 4 * 2 is 8 8 * 2 is 16 so the probability would be 1 over 16.
Why did we not get 50% heads and 50% tails?
Good point! In 2007, researchers theorised that when a coin is flipped, the flipper’s thumb imparts a slight wobble to it, causing it to spend more time with one side facing upwards while in the air and making it more likely to land showing that side.