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CaptainX
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Why tossing a coin three times is said to have binomial distribution? I'm little bit confused.
What is confusing?CaptainX said:Why tossing a coin three times is said to have binomial distribution? I'm little bit confused.
I think it's 1/2fresh_42 said:What is the probability to flip k heads in n trials?
It doesn't matter if it's a fair coin or not. Say one coin flip has probability ##p## for heads. Now what is the probability of ##k## heads in ##n## flips? How any possibilities are there for ##k## out of ##n## and what is the combined probability?CaptainX said:I think it's 1/2
... which is the answer to the question.mathman said:Binomial: prob (k successes in n trials) ##=\binom{n}{k}p^k(1-p)^{n-k}## where ##p## is the probability of success on one trial. For fair coins ##p=1/2##.
Thank you very much!mathman said:Binomial: prob (k successes in n trials) ##=\binom{n}{k}p^k(1-p)^{n-k}## where ##p## is the probability of success on one trial. For fair coins ##p=1/2##.
The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (e.g. heads or tails in coin tossing). It is represented by the formula P(x) = (n choose x) * p^x * q^(n-x), where n is the number of trials, p is the probability of success, and q is the probability of failure.
The binomial distribution is commonly used to model the outcomes of coin tossing experiments, where there are only two possible outcomes (heads or tails) and each trial is independent of the previous ones. In fact, the binomial distribution is often referred to as the "coin tossing distribution" because of its frequent use in this scenario.
The mean, or expected value, of the binomial distribution in coin tossing is equal to the number of trials (n) multiplied by the probability of success (p). In other words, if you were to toss a coin n times, the expected number of heads would be n * p.
As the number of trials increases, the shape of the binomial distribution becomes more symmetrical and bell-shaped. This is because as the number of trials increases, the probability of getting a certain number of successes becomes more evenly distributed around the mean, leading to a more normal distribution.
No, the binomial distribution is a theoretical model that describes the probability of multiple coin tosses. It cannot be used to predict the outcome of a single coin toss, as each toss is independent and has a 50% chance of either outcome regardless of previous results.