Question

A dealer selects a card at random from a standard deck of 52 cards.

a) What is the probability the card is a Queen?





b) What is the probability the card is a 5 or a 10?





c) What is the probability the card is a heart or an Ace?

Answer 1

@smokeybrown

can you help me with one last one please

Answer 2

No problem! For the first two parts:
There are 4 Queens in a standard deck (clubs, diamond, hearts, spades), so the chance of finding a queen would be "what" out of 52?
In the same way, there are 4 types of 5s and 4 types of 10s, so you can use that to find the chance of getting a 5 *or* a 10 by adding the probability of getting a 5 with the probability of getting a 10 (which would both be the same as the chance of getting a queen btw)
The third part is a little trickier, so I'll make another comment while you work on those first two

Answer 3

4/52?

Answer 4

(https://www2.southeastern.edu/Academics/Faculty/dgurney/Math241/StatTopics/Bas%20Prob.htm)

A deck of cards is 52 cards, so we'll call that "P(total number of cards)"
There are 4 suites of cards (hearts, diamonds, spades, clubs) Each of these suites have 13 cards.

so if you wanted to find a card that was a diamond from a deck of cards it would be

\[P(diamonds)=\frac{ numberof diamonds }{ total number of cards } = \frac{ 13 }{ 52 } = \frac{ 1 }{ 4 } = 0.25\]

Answer 5

Now, the probability of getting a heart is just 1/4 because there are 4 suites, each with an equal number of cards
The probability of getting an Ace you would find the same way as the probability of getting a queen
The trick is that the probability of getting an "ace or a heart" is not just adding these two together. That's because "ace" and "heart" can overlap--there's one card that is both an ace *and* a heart; if we simply add "chance of ace" and "chance of heart" we'll actually be counting the ace of hearts twice.
To counter that, what we'll actually do is:
probability(ace) + probability(heart) - probability(ace AND heart)
And that'll let you solve the third part

Answer 6

Okay soooo can't tag along for some reason sorry

Answer 7

What Smokey is saying is that a probability of getting hearts in a deck of 52 cards is \[\frac{ 1 }{ 4 }\]

And he's saying to get the probability of drawing a card that's an Ace and a heart is by using the formula:
\[P(ace)+P(heart)-P(ace.and.heart)\]

Making this be P(ace) = 4/52, and P(heart) = 13/52

Answer 8

Okay and now we do 4/52 x 13/52 or what?

Answer 9

I believe so @smokeybrown would this be true?

Answer 10

I found this

Probability of an ace is 4/52 = 1/13

Probability of a heart is 13/52 = 1/4

Probability of an ace or heart = (4+12) /52 = 4/13

Answer 11

Sorry I had to step away for a bit, but it looks like you guys got it!

Answer 12

Alrighty, I didn't want to bring out the formulas with sigma -._-.

Answer 13

okay so for number 3 it would be 1/52?

Answer 14

Nah number 3 would be the answer you found by adding the probabilities together (minus 1/52 for the ace of hearts)
You got 4/13, right? I think that's correct

Answer 15

you should probably make the answer a decimal, if that is needed

Answer 16

okay sounds good and what was for (b again?

Answer 17

b) What is the probability the card is a 5 or a 10?

Answer 18

That one would be probability(5) + probability(10), since there is no overlap between 5s and 10s, you can just add them

Answer 19

\[\frac{ 4 }{ 52 } + \frac{ 4 }{ 52 }= ?\]

Answer 20

2/13 is the answer?

Answer 21

I believe so

Answer 22

ight sweet thank you guys appreciate it alot

Answer 23

np

Answer 24

No prob!