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One hundred cards numbered 200 through 299 are placed into a bag. Afte

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Bunuel
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One hundred cards numbered 200 through 299 are placed into a bag. Afte [#permalink] New post   03 Jun 2021, 04:45
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One hundred cards numbered 200 through 299 are placed into a bag. After shaking the bag, 1 card is randomly selected from the bag. Without replacing the first card, a second card is drawn. If the first card drawn is 265, what is the probability that both cards drawn have the same tens digit?

A. 1/8

B. 1/9

C. 1/10

D. 1/11

E. 1/99
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Re: One hundred cards numbered 200 through 299 are placed into a bag. Afte [#permalink] New post   03 Jun 2021, 04:58
there are total 100 cards
after choosing 265
we have, 60 61 62 63 64 _ 66 67 68 69 , for same tens digit
choices -> 9
but now total is 99 cards left in the bag
Probability -> 9/99 -> 1/11
IMO (D)
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Re: One hundred cards numbered 200 through 299 are placed into a bag. Afte [#permalink] New post   03 Jun 2021, 04:59
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Bunuel wrote:
One hundred cards numbered 200 through 299 are placed into a bag. After shaking the bag, 1 card is randomly selected from the bag. Without replacing the first card, a second card is drawn. If the first card drawn is 265, what is the probability that both cards drawn have the same tens digit?

A. 1/8

B. 1/9

C. 1/10

D. 1/11

E. 1/99


There are 100 cards
There are 10 cards in which the tens digit is 6 (260, 261, 252, . . . 268, 269)

If the first card drawn is 265, then there are 99 cards remaining, and 9 of those cards have tens digit 6.

So, P(2nd card has tens digit 6) = 9/99 = 1/11

Answer: D
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Re: One hundred cards numbered 200 through 299 are placed into a bag. Afte [#permalink] New post   03 Jun 2021, 08:54
without replacement the 2nd card is drawn
1st card '265'
for 2nd card the tens place of 6 would :1*10*1 ; 10-1 ; 9 as 265 has been drawn
P of both cards with '6' as tens digit ; 9/99 ; 1/11
option D

Bunuel wrote:
One hundred cards numbered 200 through 299 are placed into a bag. After shaking the bag, 1 card is randomly selected from the bag. Without replacing the first card, a second card is drawn. If the first card drawn is 265, what is the probability that both cards drawn have the same tens digit?

A. 1/8

B. 1/9

C. 1/10

D. 1/11

E. 1/99
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Re: One hundred cards numbered 200 through 299 are placed into a bag. Afte [#permalink] New post   04 Jun 2021, 01:09
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The first card drawn is 265:
Cards remaining: 99
Both cards drawn have the same tens digit: 6

Possible cards are: 260, 261, 262, 263, 264, 266, 267, 268, 269.

Second card: \(\frac{9 }{ 99} = \frac{1}{11}\)

Answer D
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Re: One hundred cards numbered 200 through 299 are placed into a bag. Afte [#permalink]
04 Jun 2021, 01:09
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