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# A ticket is selected at random from 50 tickets numbered 00

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Joined: 20 Jul 2017
Posts: 1318
Location: India
Concentration: Entrepreneurship, Marketing
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A ticket is selected at random from 50 tickets numbered 00  [#permalink]

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08 Jan 2020, 09:18
1
5
00:00

Difficulty:

75% (hard)

Question Stats:

21% (01:22) correct 79% (01:14) wrong based on 33 sessions

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A ticket is selected at random from 50 tickets numbered 00, 01, 02, ……, 49. Find the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero.

A. 1/14
B. 1/10
C. 1/11
D. 1/50
E. 1/25

Posted from my mobile device
Senior Manager
Joined: 16 Feb 2015
Posts: 355
Location: United States
A ticket is selected at random from 50 tickets numbered 00  [#permalink]

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Updated on: 08 Jan 2020, 21:13
Dillesh4096 wrote:
A ticket is selected at random from 50 tickets numbered 00, 01, 02, ……, 49. Find the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero.

A. 1/14
B. 1/10
C. 1/11
D. 1/50
E. 1/25

Posted from my mobile device

Explanation:

Event A: When Sum is 8
Favorable Outcome: 08, 17, 26, 35, 44
Event B: When Product is Zero.
Fav. Outcome : 00, 01, 02,........09, 10, 20, 30, 40
A∩B = 08 (only One Case Common in Event A & B)
Required Probability = P(A/B) = P(A∩B)/P(B) = 1/50 / 14/50
=1/14

IMO-A

Originally posted by rajatchopra1994 on 08 Jan 2020, 20:31.
Last edited by rajatchopra1994 on 08 Jan 2020, 21:13, edited 1 time in total.
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Joined: 30 Nov 2019
Posts: 17
Re: A ticket is selected at random from 50 tickets numbered 00  [#permalink]

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08 Jan 2020, 21:05
1
Dillesh4096 wrote:
A ticket is selected at random from 50 tickets numbered 00, 01, 02, ……, 49. Find the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero.

A. 1/14
B. 1/10
C. 1/11
D. 1/50
E. 1/25

Posted from my mobile device

No. of favourable outcomes=08 (product of digits must also be zero so this is the only case)

=>1/50
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Re: A ticket is selected at random from 50 tickets numbered 00  [#permalink]

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10 Jan 2020, 11:38
2
Dillesh4096 wrote:
A ticket is selected at random from 50 tickets numbered 00, 01, 02, ……, 49. Find the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero.

A. 1/14
B. 1/10
C. 1/11
D. 1/50
E. 1/25

Posted from my mobile device

Of the numbers described, those whose two digits create a product of 0 are:

00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 20, 30, and 40.

Of these 14 numbers, only 08 has two digits whose sum equals 8. Therefore, the probability is 1/14.

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Joined: 13 Jan 2020
Posts: 18
A ticket is selected at random from 50 tickets numbered 00  [#permalink]

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23 Jan 2020, 05:07
1
1
Case A - Sum is 8
Possible Outcomes: 8, 17, 26, 35, 44

Case B - Product is 0
Possible Outcomes: 00, 01, 02,........09, 10, 20, 30, 40

A∩B = 08

Required Probability = P(A/B) = P(A∩B)/P(B) = $$\frac{1}{50} / \frac{14}{50}$$ = $$\frac{1}{14}$$

Ans - A
A ticket is selected at random from 50 tickets numbered 00   [#permalink] 23 Jan 2020, 05:07
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