One card is to be drawn from a deck of 52 cards. The deck includes four types of cards; red hearts, red stars, black triangles, black circles. Each type has 13 cards, numbered 1 − 13. What is the probability of drawing a red one, a black three, or a six of hearts? Give your answer as a simplified fraction.

Guest Aug 21, 2020

#1**0 **

If we make a table, we can list out all the cards.

RED Hearts: **1,2,3,4,5 ,6,7,8,9,10,11,12,13**

RED Stars: **1,2,3,4,5, 6,7,8,9,10,11,12,13**

BLACK triangles: 1,2,**3**,4,5,6,7,8,9,10,11,12,13

BLACK circles: 1,2,**3**,4,5,6,7,8,9,10,11,12,13

Now that we have a table, we see we have bolded the ones we want. We crossed out the double ones. This is the formula for or probability. So, because we are counting the one bolded (6s are bolded too, just crossed additionally). So we have there are 26 reds, and 2 blacks that fit the circumstances. Therefore the probability is 26+2=28/52 (favorable/possible) cards, and simplifying 7/13. Therefore the answer is \(\boxed{\frac{7}{13}}\)

BTW, have you noticed that guests rarely get the answers right? I have. Not to be a hypocrite.

Guest Aug 21, 2020