# If you flip three fair coins, what is the probability that you'll get all three tails?

Solution:

The outcomes of the toss of three coins are independent of each other.

The probability of getting a tail on tossing a fair coin is 1/2 .

Therefore the probability of getting tails on all the three coins is simply the product of probability of getting tails in each of the three coins:

Coin 1 Coin 2 Coin 3

P(Tails, Tails, Tails) = P(Tails) ✖ P(Tails) ✖ P(Tails)

= 1/2 ✖ 1/2 ✖ 1/2

= 1/8

**Alternative Method**

Since tossing of a coin is a Bernoulli process and can be described by a Binomial distribution the probability of the desired outcome is given by the expression below:

P(X = x) = \( C_{x}^{n}\textrm{}q^{n - x}p^{x} \)

Probability of getting three tails on the toss of a fair coin three times.

In the given problem n =3, x =3 tails ,

p =1/2 , q = 1 - p = 1 - 1/2 = 1/2

P(X = 3) = \( C_{3}^{3}\textrm{}(1/2)^{3 - 3}(1/2)^{3} \)

= 3!/(3! × 0!) × (1/2)^{0} × (1/2)^{3}

= 1 × 1 × 1/8

= 1/8

## If you flip three fair coins, what is the probability that you'll get all three tails?

**Summary:**

The probability of getting tails on all the three fair coins is 1/8.

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