SOLUTION: MAT 145: Topics In Contemporary Math Probability 2) Suppose we draw a single card from a standard deck. Find each of the following probabilities. P(ace) P(heart)

Question 1191641: MAT 145: Topics In Contemporary Math
Probability
2) Suppose we draw a single card from a standard deck. Find each of the following
probabilities.
P(ace)
P(heart)
P(Face card)
P(even red card)

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

A standard deck has 4 aces out of 52 cards total
P(ace) = 4/52 = 1/13
This is the same as remarking that we have one ace out of 13 cards of any fixed suit. Eg: there's one ace of diamonds out of 13 diamonds total.

There are 13 hearts out of 52 total
P(heart) = 13/52 = 1/4
Or you could note that we have 4 suits and one of those is hearts.

For any given suit, there are 3 face cards J, Q, K.
P(face card) = 3/13

The numbered cards are:
2,3,4,5,6,7,8,9,10
Focusing only on the even cards gets us:
2,4,6,8,10
We have 5 even numbered cards.
Double this to account for two red suits (hearts and diamonds) and we'll have 10 cards that have an even number and are red. This is out of 52 total
P(even red card) = 10/52 = 5/26

Answers:
P(ace) = 1/13
P(heart) = 1/4
P(face card) = 3/13
P(even red card) = 5/26

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