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.

Please help me figure out how to do this.

Thank you.

4 Answers

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  • Thomas
    Lv 6
    6 years ago
    Best Answer

    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.

  • 6 years ago

    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.

  • 6 years ago

    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.

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