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An experiment is to draw 1 card from a fair deck of playing cards.a) If you were to list the sample space, how many equally likely outcomes would it have? b) Find the probability of getting a 10. Leave your answer as a fraction. c) Find the probability of not getting a club. Leave your answer as a fraction. d) Find the probability of getting a diamond. Leave your answer as a fraction. e) Find the probability of getting a 10 or a diamond. Leave your answer as a fraction.

An Experiment Is To Draw 1 Card From A Fair Deck Of Playing Cardsa If You Were To List The Sample Space How Many Equally Likely Outcomes Would It Have B Find Th class=

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INFORMATION:

We have an experiment which is to draw 1 card from a fair deck of playing cards, and we must

a) If you were to list the sample space, how many equally likely outcomes would it have?

b) Find the probability of getting a 10.

c) Find the probability of not getting a club.

d) Find the probability of getting a diamond.

e) Find the probability of getting a 10 or a diamond.

STEP BY STEP EXPLANATION:

To solve the problems we need to know that a fair deck of playing cards has 52 cards in total

a) Since we have 52 different cards taking into account the number and if the card is club, diamond, heart and spade, we will have 52 outcomes which would have equally likely

b) Since we have a 10 for club, diamond, heart and spade, we have 4 favorable outcomes

Then, the probability would be

[tex]P(\text{ getting a 10})=\frac{4}{52}[/tex]

c) Since we have 13 clubs, we have 13 no favorable cases

Then, the probability would be

[tex]P(\text{ not getting a club})=1-P(\text{ getting a club })=1-\frac{13}{52}=\frac{39}{52}[/tex]

d) Since we have 13 diamonds, we have 13 favorable cases

Then, the probability would be

[tex]P(\text{ getting a diamond})=\frac{13}{52}=\frac{1}{4}[/tex]

e) We need to use the formula for Union of non-disjoint events

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Where A y B are the two events.

In our case,

A: getting a 10

B: getting a diamond

Now, replacing in the formula,

[tex]P(A\cup B)=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}[/tex]

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