Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma. 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

Question

Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma. 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

anonymous · Answer

A: 1/6
B: 1/4
C: 1/2
D: 2/12
E 3/6

anonymous · Answer

so i guess A, D
C, E

anonymous · Answer

The answer to D is incorrect. This is a reduced sample space problem. Since you know that it's a face card, it could be Jack, Queen, or King of 4 different suits, meaning the sample space is 12 cards. However, 4 of those cards are Kings. Therefore the probability of question D is 4/12, or 1/3.

I think that's why the answer isn't A/D and C/E...there's only one pair of matching probabilities.