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GOODMAN
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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?
 2 years ago
 2 years ago
GOODMAN Group Title
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?
 2 years ago
 2 years ago

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ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Okay, I'll help you with this :)
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
Thanks little bro, lol. I am studying and forgot this all.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
What would be the probability of getting a card between 2 and 9 in the first pick?
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
2/52 and 9/52
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
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 :)
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
So we have to get the ones in between?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Yes.. exactly
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Simplifying further: \( \color{Black}{\Rightarrow \Large {24 \over 52} = {12 \over 26} = {6 \over 13} }\)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Now we've picked the first. We have 1 card LESS in the deck because we haven't replaced the cards.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
There are 23 cards left that we want. 51 total cards left. \( \color{Black}{\Rightarrow \Large {23 \over 51} }\)
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
Okay...so since we had not replaced, we have to subtract 1?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Now if we want two things to happen at the same time, we shall multiply the probabilities. \( \color{Black}{\Rightarrow \Large {13 \over 26} \times {23 \over 51}}\)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
We have to subtract 1 from both numerator and denominator.
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
Wait. so after we multiply, we have to simplify further too?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Oops.. I meant this: \( \color{Black}{\Rightarrow \Large {6 \over 13} \times {23 \over 51}}\)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Multiply the fractions. The fractions are in their simplest forms so when we'll multiply it'd be in the simplest form.
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
Yes, i did that. Okay, so 46/221 is final answer?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
How did you get that?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
\( \color{Black}{\Rightarrow \Large {2 \over 13} \times {23 \over 17} }\)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Correct! :D
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
Okay, thats awesome!! Thanks soo much Parth!! Probability is my weak spot :/
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Haha probability is easy...getting the hang of what it involves is important
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
Yea, see, im reviewing this since last semester, lol.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
And I've helped someone on this site after a long time. we usually just answer questions ://
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.1
Thanks, I actually learned :D
 2 years ago
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