Question

There are 52 cards in an ordinary deck of cards. One of the four types (suits)...

There are 52 cards in an ordinary deck of cards. One of the four types (suits) is called Diamonds. What is the probability that a card randomly drawn from the deck is a King or a Diamond card?

Math   Statistics-And-Probability   
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Answer #1

Let A be the event that the card is a King

  B be the event that the card is a Diamond

A card is randomly drawn form a deck of 52 cards

To find the probability that the card is King or a Diamind, i.e., P(AUB)

We know that,

   ............ (Equation 1)

Here,

P(A) = P(the card is a King) = 4/52 .... (since, there are 4 kings in the deck of 52 cards)

P(B) = P(the card is a Diamond) = 13/52 .....(since there are 13 diamonds in the deck of 52 cards)

= P(The card is a King and also a Diamond) = 1/52 .... (since, there is one card which is both, a King as well as a Diamond)

Thus, using equation 1, we get,

Therefore, the probability that a randomly selected card is a King or a Diamond is 4/13 = 0.3077

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