Video: MATH-STATS-2018-S1-Q08

A fair coin is flipped twice. If it landed on heads the first time, what is the probability of it landing on tails in the second flip?

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Video Transcript

A fair coin is flipped twice. If it landed on heads the first time, what is the probability of it landing on tails in the second flip?

The key point that we need in order to answer this question is that flips of a coin are independent events. This means that the two events do not influence each other. So the outcome of the first event does not change the probabilities for the second. It doesn’t matter what the coin landed on in the first flip. The probability of it landing on tails in the second flip is still the same as it was regardless of what happened the first time.

We’re told in the question that this coin is fair. Which means that the probability of it landing on heads is the same as the probability of it landing on tails in each flip. So the probability of the coin landing on tails in the second flip is just half of one, which is 0.5.

This would still be true if the coin had landed on tails in the first flip. In fact, it would still be true if the coin had just landed on heads 20 times in a row. Although, at this point, you may be beginning to doubt whether or not your coin is actually fair.

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