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A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec

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Bunuel
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A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   08 Nov 2015, 09:35
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Jamboree and GMAT Club Contest Starts



QUESTION #5:

A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability that the first ball picked up is odd numbered?

(A) 0
(B) 1/3
(C) 1/2
(D) 2/3
(E) 1

Check conditions below:


Show Spoiler
For the following two weekends we'll be publishing 4 FRESH math questions and 4 FRESH verbal questions per weekend.

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, respective forum moderators will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize. He/She can opt for one of the following as a Grand Prize. It will be a choice for the winner:
-- GMAT Online Comprehensive (If the student wants an online GMAT preparation course)
-- GMAT Classroom Program (Only if he/she has a Jamboree center nearby and is willing to join the classroom program)

Bookmark this post to come back to this discussion for the question links - there will be 2 on Saturday and 2 on Sunday!



There is only one Grand prize and student can choose out of the above mentioned too options as per the conditions mentioned in blue font.
All announcements and winnings are final and no whining :-) GMAT Club reserves the rights to modify the terms of this offer at any time.


NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

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D
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   09 Nov 2015, 23:09
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We are given that, out of the three balls selected 2 are odd and 1 is even.
We can have the following arrangements: OOE, OEO, EOO
P(1st ball is odd numbered) = 2/3

Answer: D
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   08 Nov 2015, 13:59
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Probability of picking 1 even an 2 odd balls = 1/2 * 1/2 * 1/2
Now we have 2 repetitions of odd balls so we have to multiply the probability with 3!/2!
Total probability = 1/2*1/2*1/2*3
=3/8

Probability of picking the 1st ball as odd = 1/2 * 1/2 * 1/2
Now the 2nd and 3rd draw could be counted in 2! ways. Also, we need to divide the entire equation by 2! since we have 2 repetitions (odd nos). So, total probability is 1/8.

This is a conditional probability. Given that we have 2 odd and 1 even ball, what is the probability of picking the 1st ball as odd

1/8 / 3/8
1/8 * 8/3
=1/3

Answer: B
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   11 Nov 2015, 00:26
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A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability that the first ball picked up is odd numbered?

(A) 0
(B) 1/3
(C) 1/2
(D) 2/3
(E) 1

Answer-D
Selecting the balls either Even or Odd is having probability 50/100=1/2
We have already selected 3 balls with 2 odd numbers and 1 even number.
So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability is 2/3.
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   11 Nov 2015, 09:07
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The question essentially asks the probability of getting the first ball as odd out of three possible outcomes: OOE, EOO, OEO.
Here, we can see that the first ball is odd in two instances out of three.
Therefore, the probability of getting the first ball as odd is: 2/3
Ans. D
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   12 Nov 2015, 11:31
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Correct answer is D i.e. 2/3 because two odd and one even can be arranged in 3!/2!=3 ways OOE,OEO and EOO out of these only two cases are favorable. So probability will be 2/3
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   14 Nov 2015, 09:41
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Bunuel wrote:

Jamboree and GMAT Club Contest Starts



QUESTION #5:

A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability that the first ball picked up is odd numbered?

(A) 0
(B) 1/3
(C) 1/2
(D) 2/3
(E) 1

Check conditions below:


Show Spoiler
For the following two weekends we'll be publishing 4 FRESH math questions and 4 FRESH verbal questions per weekend.

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, respective forum moderators will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize. He/She can opt for one of the following as a Grand Prize. It will be a choice for the winner:
-- GMAT Online Comprehensive (If the student wants an online GMAT preparation course)
-- GMAT Classroom Program (Only if he/she has a Jamboree center nearby and is willing to join the classroom program)

Bookmark this post to come back to this discussion for the question links - there will be 2 on Saturday and 2 on Sunday!



There is only one Grand prize and student can choose out of the above mentioned too options as per the conditions mentioned in blue font.
All announcements and winnings are final and no whining :-) GMAT Club reserves the rights to modify the terms of this offer at any time.


NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

Thank you!



JAMBOBREE OFFICIAL SOLUTION:

If 3 balls are selected such that 2 of them have odd numbers on them and the other has even number, then there are 3 cases:
Odd Odd Even - OOE,
Odd Even Odd - OEO,
Even Odd Odd - EOO

Clearly, of these total 3 cases, there are 2 favorable cases in which the first ball picked is odd. Thus, required probability is 2/3.

Answer: D.
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink] New post   24 Feb 2023, 02:35
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Re: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selec [#permalink]
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