Question

A standard deck of 52 cards contains 4 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2 through 10, a jack, a queen, a king, and an ace.
Anthony decides to pick one card at random from a standard deck of 52 cards. Let A be the events that he chooses an ace and H be the event that he chooses a heart.

What is P ( A or H), the probability that the card Anthony chooses is either an ace or a heart?​

Answer 1

Answer: Our required probability is $\dfrac{4}{13}$

Step-by-step explanation:

Let A be the events that he chooses an ace.

so, P(A) = $\dfrac{4}{52}$

Let H be the events that he chooses a heart.

so, P(H) = $\dfrac{13}{52}$

We need to find P(either A or H).

So, according to rules of probability:

$P(A\cup H)=P(A)+P(H)-P(A\cap H)\\\\P(A\cup H)=\dfrac{4}{52}+\dfrac{13}{52}-\dfrac{1}{52}\\\\P(A\cup H)=\dfrac{4+13-1}{52}\\\\P(A\cup H)=\dfrac{16}{52}=\dfrac{4}{13}$

Hence, our required probability is $\dfrac{4}{13}$