question: refer to the euchre deck of cards.

Question

Refer to the euchre deck of cards. (24 cards) 4 aces, 4 kings, 4 queens, 4 jacks, 4 ten's, 4 nines.

a) What is the probability of randomly drawing

an ace or a king from a euchre deck of cards?

correct answer: P(ace or a king) = 8/24 = 1/3

b) What is the probability of randomly

drawing a red card or a diamond from

the deck?

Shouldn't the answer be P(red card or diamond) = 18/24 = 3/4 = 75%? Because the answer had said it was 50%, it's identical to a).

Answer 1

The probability of picking a diamond is:

P(diamond) = 6/24

The probability of picking a red card is:

P(red card) = P(heart) + P(diamond) = 6/24 + 6/24 = 12/24 = 1/2

So you can see that the probability of picking a diamond is already included in the probability of picking a red card. No need to count it again.