Question

A card is drawn randomly from a standard deck of cards. You win $5 if the card is adiamond or a king. What is the probability that you will win 5 dollars?

Answer 1

EXPLANATION

Let name event A as the event of drawing a Diamond and let us name event B as the event of drawing an King.

Now, we are required to find P(A union B)

We know that P(A union B) = P(A) + P(B) - P(A intersection B) … (i)

Let's suppose there are 52 cards in a standard deck.

A standard deck of cards has 13 diamonds and 4 kings

We have P(A) = 13/52 = 1/4, P(B) = 4/52 = 1/13

A intersection B denotes the case of the King of Diamonds whose probability = 1/52

Now plugging in these values to equation (i) and simplifying, we obtain the required probability as P(A union B) = 1/4 + 1/13 - 1/52 = 4/13

The probability is 4/13 or 0.307 or 30.7%