If you flip a coin 30 times and get heads 11 times
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If you're seeing this message, it means we're having trouble loading external resources on our website. Show If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Welcome to the coin flip probability calculator, where you'll have the opportunity to learn how to calculate the probability of obtaining a set number of heads (or tails) from a set number of tosses. This is one of the fundamental classical probability problems, which later developed into quite a big topic of interest in mathematics. For example, maybe you like Batman, and know of one of his many villains, Two-Face? You'd think that his name comes from the fact that half of his face is burnt, but no! (Okay, maybe a little bit.) He has a lucky coin that he always flips before doing anything. As this coin has two faces on it, his coin toss probability of getting a head is 1. Better not get on the wrong side (or face) of him! 🙋 If you're interested in the probability of runs in coin flips, visit our dedicated coin toss streak calculator. Classical probabilityThe probability of some event happening is a mathematical (numerical) representation of how likely it is to happen, where a probability of 1 means that an event will always happen, while a probability of 0 means that it will never happen. Classical probability problems often need to you find how often one outcome occurs versus another, and how one event happening affects the probability of future events happening. When you look at all the things that may occur, the formula (just as our coin flip probability formula) states that
Take a die roll as an example. If you have a standard, 6-face die, then there are six possible outcomes, namely the numbers from 1 to 6. If it is a fair die, then the likelihood of each of these results is the same, i.e., 1 in 6 or But what if you repeat an experiment a hundred times and want to find the odds that you'll obtain a fixed result at least 20 times? Let's look at another example. Say that you're a teenager straight out of middle school and decide that you want to meet the love of your life this year. More specifically, you want to ask ten girls out and go on a date with only four of them. One of those has got to be the one, right? The first thing you have to do in this situation is look in the mirror and rate how likely a girl is to agree to go out with you when you start talking to her. If you have problems with assessing your looks fairly, go downstairs and let your grandma tell you what a handsome, young gentleman you are. So a solid As you only want to go on four dates, that means you only want four of your romance attempts to succeed. This has an outcome of How to calculate probability?"Hey man, but girls and coins are two different things! I should know, I've seen at least one of each." Well, let me explain that these two problems are basically the same, that is, from the point of view of mathematics. Whether you want to toss a coin or ask a girl out, there are only two possibilities that can occur. In other words, if you assign the success of your experiment, be it getting tails or the girl agreeing to your proposal, to one side of the coin and the other option to the back of the coin, the coin toss probability will determine the answer. It all boils down to getting your hands on a coin that is weighted appropriately. Mathematically, we talk about the binomial probability distribution. Let's look at a step-by-step example to see how to calculate the probability of an event using the coin toss probability calculator: What is the probability of getting 11 heads in a row?Since each coin toss has a probability of heads equal to 1/2, I simply need to multiply together 1/2 eleven times. That's a 0.05% chance of flipping eleven heads in a row!
What is the probability of getting heads 30 times in a row?That's a lot more likely: the likelihood of getting a string of 30 heads in a row somewhere in your 100 flips is about 1 in 30 million. If there are at least 30 million people in the world who have flipped a coin 100 times, it shouldn't be surprising if one of them has flipped 30 heads in a row at some point.
What is the probability of getting heads when flipping a coin 20 times?The probability of event A is generally written as P(A).
The probability of getting heads is half. You might already know that the probability is half/half or 50% as the event is an equally likely event and is complementary so the possibility of getting heads or tails is 50%.
What is the probability of getting 10 heads in 10 flips?Junho: According to probability, there is a 1/1024 chance of getting 10 consecutive heads (in a run of 10 flips in a row).
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