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GOODMAN
 3 years 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?
GOODMAN
 3 years 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?

This Question is Closed

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

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

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1No...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 :)

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

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

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

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

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Now 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
 3 years ago
Best ResponseYou've already chosen the best response.1We have to subtract 1 from both numerator and denominator.

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

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

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

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1How did you get that?

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

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

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

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

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

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