Question

Find the probability of: (a) Drawing either a jack or a spade from a regular deck of cards. (b) Drawing either a

face card (jack, queen, or king) or a diamond from a regular deck of cards.

Answer 1

a) 4/13

b) 11/26

Explanation:

a)

so, there are 4 jacks in a deck, and 13 spades

however, there is 1 spade jack [this is overlap], so we need to subtract one from our total of cards.

4 + 13 = 17 - 1 = 16

16/52

(a card deck typically has 52 cards)

we can simplify this fraction to be 4/13

probability can be written many ways, but there is a 4/13 probability --you can transform this fraction into different forms if you need

b)

similar to the last one, we want to add up our selected terms (face cards and diamonds)

there are 13 diamonds in a deck, and 3 face cards from each suit ( 3 x 4 = 12)

however, there is an overlap of face cards and diamonds-- the 3 diamond facecards

so,

13 + 12 = 25 - 3 = 22

22/ 52 = 11/26

so this is simplified to 11/26

hope this helps!

if you would like, I can specifically add P(...) if that would clarify things (just let me know :) )