## andijo76 3 years ago 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 4 on two fair six sided dice B. drawing a black seven out of a standard 52 card deck given it’s not a face card or an Ace. C. rolling a sum of 11 on two fair six sided dice D. rolling a sum of 7 on two fair six sided dice E. drawing a three out of a standard 52 card deck given it’s not a face card or an Ace.

1. satellite73

wow this is maybe the 4th time i have seen this exact problem. where does it come from?

2. satellite73

we can do the dice first $P(A)=\frac{3}{36}=\frac{1}{12}$ since you can roll (3,1), (2,2), (1,3)

3. satellite73

$P(C)=\frac{2}{36}=\frac{1}{18}$ possible rolls are (5,6), (6,5)

4. satellite73

$P(D)=\frac{6}{36}=\frac{1}{6}$ and that takes care of the dice

5. satellite73

deck has 12 face cards and 4 aces so you know it is not one of those 16 cards and must be one of the remaining 36 cards. there are 2 black sevens, so probability of picking a 7 if you know it is not one of the above 16 cards is $\frac{2}{36}=\frac{1}{18}$