# What pair has equally likely outcomes?

#### aburchett

##### New member
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
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?