- anonymous

Two cards are drawn from a standard deck of 52 cards without replacement. What is the probability that both cards are greater than 2 and less than 9?

- schrodinger

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- ParthKohli

Okay, I'll help you with this :)

- anonymous

Thanks little bro, lol. I am studying and forgot this all.

- ParthKohli

What would be the probability of getting a card between 2 and 9 in the first pick?

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## More answers

- anonymous

2/52 and 9/52

- ParthKohli

No...it's saying that it's greater than 2 and less than 9. 3,4,5,6,7,8 are the numbers that qualify for me :)

- anonymous

So we have to get the ones in between?

- ParthKohli

Yes.. exactly

- ParthKohli

Since there are 3,4,5,6,7,8 in four suits, the probability would be:
\( \color{Black}{\Rightarrow \Large {4 \times 6 \over 52} }\)
For the first pick.

- ParthKohli

Simplifying further:
\( \color{Black}{\Rightarrow \Large {24 \over 52} = {12 \over 26} = {6 \over 13} }\)

- ParthKohli

Now we've picked the first. We have 1 card LESS in the deck because we haven't replaced the cards.

- ParthKohli

So this time the denominator of the probability would become 51. The numerator will also get one less because we have assumed that we have picked one card which is 3,4,5,6,7 or 8.

- ParthKohli

There are 23 cards left that we want. 51 total cards left.
\( \color{Black}{\Rightarrow \Large {23 \over 51} }\)

- anonymous

Okay...so since we had not replaced, we have to subtract 1?

- ParthKohli

Now if we want two things to happen at the same time, we shall multiply the probabilities.
\( \color{Black}{\Rightarrow \Large {13 \over 26} \times {23 \over 51}}\)

- ParthKohli

We have to subtract 1 from both numerator and denominator.

- anonymous

Thats it?

- ParthKohli

Nope

- anonymous

Wait. so after we multiply, we have to simplify further too?

- ParthKohli

Oops.. I meant this:
\( \color{Black}{\Rightarrow \Large {6 \over 13} \times {23 \over 51}}\)

- ParthKohli

Multiply the fractions. The fractions are in their simplest forms so when we'll multiply it'd be in the simplest form.

- anonymous

Yes, i did that. Okay, so 46/221 is final answer?

- ParthKohli

How did you get that?

- ParthKohli

Oh yes

- ParthKohli

\( \color{Black}{\Rightarrow \Large {2 \over 13} \times {23 \over 17} }\)

- ParthKohli

Correct! :D

- anonymous

Okay, thats awesome!! Thanks soo much Parth!! Probability is my weak spot :/

- ParthKohli

Haha probability is easy...getting the hang of what it involves is important

- anonymous

Yea, see, im reviewing this since last semester, lol.

- ParthKohli

And I've helped someone on this site after a long time. we usually just answer questions ://

- anonymous

Thanks, I actually learned :D

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