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# What is the Probability of Flipping a Coin Three Times and having them all Land "Heads" up?

**Solution:**

The probability of getting a head on tossing a coin is 1/2. Therefore

The marginal probability of getting a heads = P(H) = 1/2

If the coin is tossed three times then the probability of getting heads each time is :

P(H) × P(H) × P(H) = (1/2) × (1/2) × (1/2) = 1/8

Each of the three tosses is an independent event and hence their probabilities can be multiplied to give the probability of getting heads in each of the three tosses.

**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 heads on the toss of a fair coin three times.

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

## What is the Probability of Flipping a Coin Three Times and having them all Land "Heads" up?

**Summary:**

The probability of Flipping a Coin Three Times and having them all Land "Heads" up is 1/8.

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