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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?

Mathematics
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Okay, I'll help you with this :)
Thanks little bro, lol. I am studying and forgot this all.
What would be the probability of getting a card between 2 and 9 in the first pick?

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Other answers:

2/52 and 9/52
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 :)
So we have to get the ones in between?
Yes.. exactly
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.
Simplifying further: \( \color{Black}{\Rightarrow \Large {24 \over 52} = {12 \over 26} = {6 \over 13} }\)
Now we've picked the first. We have 1 card LESS in the deck because we haven't replaced the cards.
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.
There are 23 cards left that we want. 51 total cards left. \( \color{Black}{\Rightarrow \Large {23 \over 51} }\)
Okay...so since we had not replaced, we have to subtract 1?
Now if we want two things to happen at the same time, we shall multiply the probabilities. \( \color{Black}{\Rightarrow \Large {13 \over 26} \times {23 \over 51}}\)
We have to subtract 1 from both numerator and denominator.
Thats it?
Nope
Wait. so after we multiply, we have to simplify further too?
Oops.. I meant this: \( \color{Black}{\Rightarrow \Large {6 \over 13} \times {23 \over 51}}\)
Multiply the fractions. The fractions are in their simplest forms so when we'll multiply it'd be in the simplest form.
Yes, i did that. Okay, so 46/221 is final answer?
How did you get that?
Oh yes
\( \color{Black}{\Rightarrow \Large {2 \over 13} \times {23 \over 17} }\)
Correct! :D
Okay, thats awesome!! Thanks soo much Parth!! Probability is my weak spot :/
Haha probability is easy...getting the hang of what it involves is important
Yea, see, im reviewing this since last semester, lol.
And I've helped someone on this site after a long time. we usually just answer questions ://
Thanks, I actually learned :D

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