How do you find the probability of obtaining at least one tail when a coin is tossed five times?

Answer 1

#1 - 1/32 = 31/32#

'At least one tail' means that there can be one, or two or three or four or five tails.

The only option that is not included is five heads.

The sum of all the probabilities is always #1#.
#P("at least one tail") = 1 - P("no tail")#
#P("no tail") = P("all heads") = P("H,H,H,H,H")#
In any throw the probability of a tail or a head is #1/2#
#P("H,H,H,H,H") = 1/2xx1/2xx1/2xx1/2xx1/2 = (1/2)^5 = 1/32#
#P("at least one tail") = 1 - 1/32 = 31/32#
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Answer 2

To find the probability of obtaining at least one tail when a coin is tossed five times, you can use the complement rule.

The probability of obtaining at least one tail is equal to 1 minus the probability of getting all heads in five tosses.

The probability of getting all heads in five tosses is ( (1/2)^5 ), since the probability of getting heads on one toss of a fair coin is (1/2).

Therefore, the probability of obtaining at least one tail in five tosses is (1 - (1/2)^5), which equals (1 - 1/32 = 31/32).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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