What is the probability that a five-card poker hand contains the ace of hearts?

Solution:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

A deck of 52 cards contains 4 suits: spades, club, hearts and diamonds, each containing 13 cards.

We have to find the probability of a five-card poker hand that contains the ace of hearts.

Required probability = 1 - (probability of the hand not containing the ace of hearts)

Probability of the hand not containing the ace of heart

= \(\frac{51}{52}\times \frac{50}{51}\times \frac{49}{50}\times \frac{48}{49}\times \frac{47}{48}\)

= 0.9038

Required probability = 1 - 0.9038 = 0.0962

Therefore, the probability of the hand that contains the ace of heart is 0.0962

What is the probability that a five-card poker hand contains the ace of hearts?

Summary:

The probability that a five-card poker hand contains the ace of hearts is 0.0962