If you flip a fair coin 10 times. What is the probability of getting at least one tail?

Solution:

Given, a fair coin is flipped 10 times.

We have to find the probability of getting at least one tail.

Probability of getting at least one coin is the complement of 1 minus the probability

Probability that tail will occur when a coin is flipped is given by

p = 1 / 2 

The probability of getting at least one tail is equal to one minus the probability of all heads.

P = 1 - (1 / p)¹⁰

The probability of head all 10 times is (1 / 2)¹⁰

(1 / 2)¹⁰ = 1 / 1024

Now,

P = 1 - (1 / p)¹⁰ = 1 - (1 / 1024)

= (1024 - 1) / 1024

P = 1023 / 1024

Therefore, the probability of getting at least one tail is 1023 / 1024.

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If you flip a fair coin 10 times. What is the probability of getting at least one tail?

Summary:

If you flip a fair coin 10 times. The probability of getting at least one tail is 1023 / 1024.