#Coin flip probability calculator trial#

#Coin flip probability calculator trial#

We have to classify each trial outcome as a success or failure - again, going back to the original question, it asked “…how many times would you expect the coin to land heads up?” When asked this way, each trial (flip) that ends in a head is a success, while a tail would be a failure. The original question was “If you flipped a fair coin 10 times, how many times would expect the coin to land heads up?” In this question, the number of trials is fixed at 10. The number of trials (flips, rolls, etc.) is fixed - The number of times you are going to flip a coin or roll the dice are fixed, or determined in advance. The fourth flip would still have the same probability (50% head, 50% tail) as the prior flips. You could say “a coin has no memory.” If you were to flip a coin three times in a row and all three were tails, the coin has no memory of that. No coin flip affects the outcome of another coin flip. The second flip would have the same chance of coming up a head on the second flip if the first flip was a head than it would if the first flip was a tail. The trials are independent - If we flipped a coin, and it came up heads, then flipped it a second time, the second flip would not be affected by the outcome of the first flip. In reality, we are likely only to get exactly 5 heads about 1 in every 4 times.įlipping a coin or rolling dice have a special probability distribution associated with their outcomes called a “binomial distribution.” The Elements of a Binomial Distribution While the most likely outcome is 5, we have to contend with random error, or chance. Next, you would multiply the 0.5 (same as 50%) by 10 (number of coin flips) and get your answer, which would be 5 (the expected value). Heads is 1 of 2 outcomes, so there would be a 50% probability of the outcome being a head and a 50% probability of the outcome being a tail. A fair coin can land either with the heads up, or the tails up. How would you answer the question, “If you flipped a fair coin 10 times, how many times would expect the coin to land heads up?” (assuming a two-sided coin, with one side denoted as heads, the other tails).Ī logical way to work through this problem would be to first think of what the probability of the coin landing heads up is.

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