SOLVED: What is the probability of obtaining at least one tail when a coin is flipped six times?

Video Transcript

once again, i welcome to a modern trouble this time, we ‘re dealing with probability, distributions we ‘re dealing with probability distributions and, for the most part, the concern type of probability. distribution is the binomial probability distribution. So we ‘re looking at the binomial probability, distribution and sealed distinctions happen with the binomial probability distributions. We have the probability of success being p and the probability of failure being the compliment which is 1 subtraction p. besides, the number of trials the numeral of trials is fixed. So we have a sterilize number of trials and each trial has 2 outcomes, so each trial happens to have 2 outcomes and of course, the each consequence is independent from from each and every other consequence. so each result is independent from each and every early result. The typical binomial probability formula is then hundred x, phosphorus raised to x, 1 minus bacillus, raised to x and minus ten, where north is the sample size adam is the probability or rather of probability. Let ‘S barely say. Let ‘S just say, the number of trials are of interest. This is the count of childs of sake and then, of class, phosphorus is the probability of success. 1. Minus p is the probability of bankruptcy. We’Re looking at a new problem and in this especial problem were concern in. We want to determine determine the probability of lack to determine the probability of obtaining the probability of obtaining at least at least 1 dock when a coin is flipped when a mint is flipped 6 times. then when we flip the mint 6 times, it means nitrogen equals to 6 and then the probability of getting at least 1 tail. That means ten is greater than or equal to 1. This means we have a probability of 1 plus so ten, equals to 1 plus probability that adam equals to 2 plus probability that ten equals to 3 plus probability that adam equals to 4 plus probability that x equals to 5 and, of course probability that x equals To 6, a first way of getting this probability would be to take the compliment and subtract the probability of zeal. So this is 1 minus. If we ‘re using newton c ten, p of x, 1 minus farad of ten, this would be 1. Minus normality is 6 times c to 0 charge probability of success is .5 raised to x, which is 0 equitable clarification. This is n minus adam and then probability of paliar is besides 1 half commend, you ‘re tossing a coin. so for a coin, probability of heads is 1 half and probability of tales is besides 1 half these 2 events happened to be independent, so they ‘re mugwump events, so we ‘re looking at at least 1 tail and then north is 6 subtraction point. This is going to be 1 minus, so we have to do the probability for 0 and we ‘re looking at the computations for the probability when it ‘s 0 and that ‘s going to give us the same value as zegoso. This is 0.015625015625. So we just want to make certain that those are the probabilities that we ‘re dealing with. sol then we have. We have these probabilities. We want to subtract the probability from 1, and thus the consequence that we get in terms of probability to get at least 1 tail is going to be 0.984398. .4375. I hope you enjoy the problem, feel free to send any questions or comments and have a fantastic day.

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