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One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ...,

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Bunuel
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One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink] New post   27 Jan 2021, 14:49
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One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., 98, 99. If X is defined as sum of digits and Y as product of the digits, what is the probability that X = 9, given Y = 0?

A. 10/19
B. 2/19
C. 1/10
D. 2/100
E. 1/100


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unraveled
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One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink] New post   Updated on: 13 Feb 2021, 20:44
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Bunuel wrote:
One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., 98, 99. If X is defined as sum of digits and Y as product of the digits, what is the probability that X = 9, given Y = 0?

A. 10/19
B. 2/19
C. 1/10
D. 2/100
E. 1/100


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Y = 0 for 00, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 01, 02, 03, 04, 05, 06, 07, 08, 09
Total 19 cases.
X = 9 only for 2 cases i.e. 09 and 90.

P(X=9, Y=0) = 2/19 = 2/19.

Answer B.

Originally posted by unraveled on 28 Jan 2021, 00:12.
Last edited by unraveled on 13 Feb 2021, 20:44, edited 2 times in total.
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Re: One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink] New post   28 Jan 2021, 00:26
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X = 9, for 10 cases
Y = 0 for 20 cases

Probability that X = 9, given Y = 0 =>\(\frac{10}{100}\)*\(\frac{20}{100}\) = \(\frac{2}{100}\)

IMO Option D
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Re: One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink] New post   29 Jan 2021, 13:54
Y is 0 for 19 cases :00 01 02 03 04 05 06 07 08 09 10 20 30 40 50 60 70 80 90
X is 9 for only 2 cases :09 90
probability of X=9 given Y =0 is 2/19 (IMO)
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Re: One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink] New post   30 Jan 2021, 09:18
Unravel

Quote:
Y = 0 for 00, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 01, 02, 03, 04, 05, 06, 07, 08, 09
Total 20 cases.
X = 9 only for 2 cases i.e. 09 and 90.

P(X=9, Y=0) = 2/20 = 1/10.



Are there total 20 cases or 19 cases?
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Re: One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink] New post   30 Jan 2021, 21:48
There are 100 cases, it appears. 00, 01, 02, ... ,98,99

The product must be zero and sum to 9.

There are two cases, 09, 90.

2/100
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Re: One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink] New post   29 Nov 2022, 11:50
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Re: One ticket is selected from 100 tickets numbered 00, 01, 02, 03, ..., [#permalink]
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