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.