Question Video: Finding the Probability of Getting Tails at Least Once upon Flipping a Coin Three Times | Nagwa Question Video: Finding the Probability of Getting Tails at Least Once upon Flipping a Coin Three Times | Nagwa

# Question Video: Finding the Probability of Getting Tails at Least Once upon Flipping a Coin Three Times Mathematics

What is the probability of getting tails at least once if a coin is flipped three times?

02:48

### Video Transcript

What is the probability of getting tails at least once if a coin is flipped three times?

Finally, all three coins could land on heads. This means that there are eight different combinations that could occur. We want the probability of getting tails at least once. Our top combination has three tails. The next three have two tails. The three combinations after this have one coin landing on tails. This means that seven out of the eight combinations end up with getting tails at least once. The probability of this occurring is therefore seven out of eight or seven-eighths.

An alternative method would be to calculate the probability of the only combination we don’t want first, the probability of three heads. The probability of landing on heads in any individual toss of a coin is one-half. As each of the events or tosses are independent, we can multiply these fractions to calculate the probability of getting three heads. The probability of three heads is one-eighth. As the probability of getting tails at least once is everything else, we can subtract this answer from one as we know probabilities sum to one. Subtracting one-eighth from one, once again, gives us an answer of seven-eighths. When flipping a coin three times, the probability of getting tails at least once is seven-eighths.

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