# A single card is drawn from a deck. Find the probability of selecting a heart or a diamond or a jack or an Ace?

Statistic question that I cannot figure out

A) .5769

B) .6538

C) .482

D) .123

I got

0.05769 and then 0.634 when I did the problem another way.

Thank you.

Relevance

Well, you just find each and add them together.

Heart = (13/52) or (1/4)

Diamond = Same as Heart

Jack = (4/52) or (1/13)

Ace = Same as Jack

The thing you have to watch for, is the ones that collide. Jack of hearts, jack of diamonds, etc ..

Hearts: 13

Diamonds: 13

Jacks: 2

Aces: 2

There, we removed the two red jacks and aces.

(13 / 52) + (13 / 52) + (2 / 52) + (2 / 52) = 30 / 52 = .576923

Note that you should see an obvious wrong when you're choosing over half the deck, and getting an answer of 5%. I assume that may be why you're asking, but thought it'd be good to point out.

• There are 13 hearts and 13 diamonds; there are 4 jacks and 4 aces, but 2 of the jacks and aces

have already been counted as hearts/diamonds - so there are 4 cards to be counted here,

plus the 26 hearts diamonds. Prob. is 30/52=.5769.

• There are 13 hearts and 13 diamonds = 26

In addition there are 4 more cards in the group Jack of spades, Jack of Clubs, Ace of spades, Ace of Clubs

That makes a total of 30 cards

The probability therefore is 30/52 = Answer A = 0.5769

• Number of hearts = 13

Number of diamonds = 13

Number of aces = 2 (actual number of aces are 4 but we have already included 2 aces in packs of

hearts and diamonds)

Number of jacks = 2 (actual number of jacks are 4 but we have already included 2 jacks in packs of

hearts and diamonds)

Therefore probability = (13 + 13 + 2 + 2) / 52

= 30 / 52

= 0.5769

Hope this helps you.