• Welcome! The new FreeMathHelp.com forum is live. We've moved from VB4 to Xenforo 2.1 as our underlying software. Hopefully you find the upgrade to be a positive change. Please feel free to reach out as issues arise -- things will be a little different, and minor issues will no doubt crop up.

What pair has equally likely outcomes?

aburchett

New member
Joined
Jan 19, 2011
Messages
48
Which pair has equally likely outcomes? Check the two choices below which have equal probabilities of success. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards).

a) rolling a sum of 7 on two fair six sided dice
b) drawing a diamond out of a standard 52 card deck
c) drawing a black card out of a standard 52 card deck
d) drawing a king out of a standard 52 card deck given it’s a face card.
e) rolling a 2, 3 or 4 on one fair six sided die

My work:
a) 1+6=7, 2+5=7, 3+4=7, 4+3=7, 5+2=7, 6+1=7 There are a total of 36 possiblities, so 7/36

b) In a standard deck diamonds are A,2,3,4,5,6,7,8,9,10,J,Q,K which is 13/52

c) half of the cards in a standard deck are black, so 26/52 or 1/2

d) There are 4 Kings in a standard deck of cards, there are 4 face cards in each deck and 4 suits=16 possibilities, 4/16 or 1/4

e) 2,3 or 4 are 3 out of 6 numbers on a die, so 3/6 or 1/2

So c) and e) are the pair that have equally likely outcomes? Is this correct?
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,091
aburchett said:
Which pair has equally likely outcomes? Check the two choices below which have equal probabilities of success. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards).

a) rolling a sum of 7 on two fair six sided dice
b) drawing a diamond out of a standard 52 card deck
c) drawing a black card out of a standard 52 card deck
d) drawing a king out of a standard 52 card deck given it’s a face card.
e) rolling a 2, 3 or 4 on one fair six sided die

My work:
a) 1+6=7, 2+5=7, 3+4=7, therefore 3 sets of numbers out of the 6 numbers will equal 7, so 3/6 or 1/2

There are 36 ways a pair of dice can be thrown.

Sum seven will come for 6 of those ? probability 6/36 = 1/6


b) In a standard deck diamonds are A,2,3,4,5,6,7,8,9,10,J,Q,K which is 13/52

c) half of the cards in a standard deck are black, so 26/52 or 1/2

d) There are 4 Kings in a standard deck of cards, so 4/52 or 1/13

e) 2,3 or 4 are 3 out of 6 numbers on a die, so 3/6 or 1/2

Obviously I did something wrong, because you are supposed to be able to pick a pair that have equally likely outcomes and I have 3 that all end up equaling 1/2, can you help me and tell me where I screwed up?
 
Top