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One ticket is selected at random from 50 tickets numbered 0, 0

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ashwini2k6jha
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One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 19:12
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

19% (01:49) correct 81% (01:00) wrong based on 36 sessions
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answer:A
only possible digit is 08
total number of digit=50
hence probability=1/50

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D
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 19:13
Fact 1:
Product of the digits on the tickets is Zero.
Sample set = (00,01,02,03,04,05,06,07,08,09,10,20,30,40) = 14 values

Fact 2:
Sum of the digits is 8.
Only valid scenario is 08 from the given set.

Probability = 1/14

Option D
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 19:14
two events
A={8,17,26,35,44}
B={00,01,02,03,....40}

p(A/B)=P(A and B)/P(B)
1/50/14/50
1/14

Ans D
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 19:15
Answer: A
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 19:16
IMO A
Let the digits be (ab)

axb=0
a+b=8

For a x b =0, either a=0 0r b=0

if a=0, b=8 , number =08 (0k)
But if b=0, a=8 number = 80 (not possible)

so , required number = 08 (Count = 1)

Probability = 1/50
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 19:21
since there are only 14 numbers which will give the product of the digits as 0 (0, 01,...) and 08 is the only number which sums to 8, so the probability is 1/14
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 19:39
Option A
Attachments

IMG_20200712_074520.jpg
IMG_20200712_074520.jpg [ 100.64 KiB | Viewed 738 times ]

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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 20:26
The number for which product is 0 & sum is 8 = 08
Ways to select 08=01
Ways to select any number=50C1

Probability=1/50c1= 1/50

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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 20:53
List out all the possibilities, numbers with digit sum of 8 can be written as {08,17,26,35,44}

Then numbers with a product of 0 can be written as {01, 02, 03, 04, 05, 06, 07, 07 ,09}

Total possibilities in both sets is equal to 14 and only one overlaps so desired prob. is 1/14.

Option D.
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   11 Jul 2020, 22:56
Out of 50 numbers, only one ticket 08 satisfy the condition i.e the sum is 8 and the product is zero.

Answer is 1/50
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   12 Jul 2020, 00:30
Favorable outcome = 1 (08)
Total outcomes = 50
Probability = 1/50
Hence, OA is (A).
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   12 Jul 2020, 00:43
only one number is possible that is 08 so 1/50
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   Updated on: 12 Jul 2020, 01:13
There is only one number 08 for which the product of the digits will be 0 and sum is 8.

Total cases 0,01,02,03,04,05,06,07,08,09,10,20,30,40.

1/14

Originally posted by warrior1991 on 12 Jul 2020, 01:11.
Last edited by warrior1991 on 12 Jul 2020, 01:13, edited 1 time in total.
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   12 Jul 2020, 01:13
2 no.s - a and b

a + b= 8
a*b= 0
either, a is 0 or b is 0, since no. 80 does not exist on any ticket therefore only option is = 08
probability = 1/50
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   12 Jul 2020, 01:14
Out of 50 tickets only one pair satisfies the give condition. (08- ticket no= so proab = 1/50)
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   12 Jul 2020, 01:14
2 no.s - a and b

a + b= 8
a*b= 0
either, a is 0 or b is 0, since no. 80 does not exist on any ticket therefore only option is = 08
probability = 1/50
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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink] New post   12 Jul 2020, 01:24
OA = A

Only possible number is 08 because sum is 8 and since product is 0, number must include 0.

So 1/50 is the probability

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Re: One ticket is selected at random from 50 tickets numbered 0, 0 [#permalink]
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