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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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ParthKohliBest ResponseYou've already chosen the best response.1
Okay, I'll help you with this :)
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Thanks little bro, lol. I am studying and forgot this all.
 one year ago

ParthKohliBest 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?
 one year ago

ParthKohliBest 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 :)
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
So we have to get the ones in between?
 one year ago

ParthKohliBest 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.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Simplifying further: \( \color{Black}{\Rightarrow \Large {24 \over 52} = {12 \over 26} = {6 \over 13} }\)
 one year ago

ParthKohliBest 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.
 one year ago

ParthKohliBest 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.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
There are 23 cards left that we want. 51 total cards left. \( \color{Black}{\Rightarrow \Large {23 \over 51} }\)
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Okay...so since we had not replaced, we have to subtract 1?
 one year ago

ParthKohliBest 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. \( \color{Black}{\Rightarrow \Large {13 \over 26} \times {23 \over 51}}\)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
We have to subtract 1 from both numerator and denominator.
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Wait. so after we multiply, we have to simplify further too?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Oops.. I meant this: \( \color{Black}{\Rightarrow \Large {6 \over 13} \times {23 \over 51}}\)
 one year ago

ParthKohliBest 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.
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Yes, i did that. Okay, so 46/221 is final answer?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
How did you get that?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
\( \color{Black}{\Rightarrow \Large {2 \over 13} \times {23 \over 17} }\)
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Okay, thats awesome!! Thanks soo much Parth!! Probability is my weak spot :/
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Haha probability is easy...getting the hang of what it involves is important
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Yea, see, im reviewing this since last semester, lol.
 one year ago

ParthKohliBest 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 ://
 one year ago

GOODMANBest ResponseYou've already chosen the best response.1
Thanks, I actually learned :D
 one year ago
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