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# Each of the cards in a deck of 50 cards has a number from 1 to 20

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Senior Manager
Joined: 22 Jun 2016
Posts: 250
Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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25 Jun 2016, 05:23
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85% (hard)

Question Stats:

54% (01:38) correct 46% (02:06) wrong based on 109 sessions

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Each of the cards in a deck of 50 cards has a number from 1 to 20 written on it in either black, red or blue ink. If one card is to be selected at random from the deck, what is the probability that the card selected will either have an odd number or be written in red ink?

(1) The probability that the card will both have an off number and be written in red ink is 0.

(2) The probability that the card will have an odd number minus the probability that the card will be written in red ink is 0.4

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Senior Manager
Joined: 22 Jun 2016
Posts: 250
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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26 Jun 2016, 05:56
3
For those of you who were not able to answer this, here is the answer.
We know there are cards written with numbers in different probability colours. We are asked for the probability of randomly selecting a card that has either an odd or is written in red. Let us assume this prob to be x.

So, x= (prob of selecting a card with an odd number) + (prob of selecting a card written in red) - (prob of selecting a card with an odd number written in red)
or we can write the above as: x = P(odd) + P(red) - P(odd and red).

Statement 1: P(odd and red) = 0

Insufficient as we don't know P(odd) + P(red).

Statement 2: P(odd) - P(red) = 0.4

This can be true for various combination of P(odd) and P(red), for ex. P(odd)=0.5 and P(red)=0.1 or P(odd)=0.6 and P(red)=0.2 etc.

Hence, statement 2 is also insufficient!

Combining 1 and 2 also we do not have exact value of P(odd) and P(red). We just have values for P(odd)-P(red) and P(odd and red).

Therefore, the answer will be E.

--------------------------------------

P.S. Don't forget to give kudos
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Manager
Joined: 14 May 2014
Posts: 71
Location: India
GMAT 1: 680 Q49 V31
GPA: 3.44
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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26 Jun 2016, 08:07
14101992 wrote:
For those of you who were not able to answer this, here is the answer.
We know there are cards written with numbers in different probability colours. We are asked for the probability of randomly selecting a card that has either an odd or is written in red. Let us assume this prob to be x.

So, x= (prob of selecting a card with an odd number) + (prob of selecting a card written in red) - (prob of selecting a card with an odd number written in red)
or we can write the above as: x = P(odd) + P(red) - P(odd and red).

Statement 1: P(odd and red) = 0

Insufficient as we don't know P(odd) + P(red).

Statement 2: P(odd) - P(red) = 0.4

This can be true for various combination of P(odd) and P(red), for ex. P(odd)=0.5 and P(red)=0.1 or P(odd)=0.6 and P(red)=0.2 etc.

Hence, statement 2 is also insufficient!

Combining 1 and 2 also we do not have exact value of P(odd) and P(red). We just have values for P(odd)-P(red) and P(odd and red).

Therefore, the answer will be E.

--------------------------------------

P.S. Don't forget to give kudos

Quite not understood the logic
x = P(odd) + P(red) - P(odd and red).
1) says P(odd and red)=0
so x = P(odd) + P(red) - 0= x = P(odd) + P(red)

2) says
P(odd)- P(Red)=0.4
P(odd)= 0.5 so P(red)=0.1

combine 1 and 2

x= 0.5+0.1=0.6

are we not getting a value here?
Current Student
Joined: 18 Oct 2014
Posts: 882
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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26 Jun 2016, 10:03
RatneshS wrote:
14101992 wrote:
For those of you who were not able to answer this, here is the answer.
We know there are cards written with numbers in different probability colours. We are asked for the probability of randomly selecting a card that has either an odd or is written in red. Let us assume this prob to be x.

So, x= (prob of selecting a card with an odd number) + (prob of selecting a card written in red) - (prob of selecting a card with an odd number written in red)
or we can write the above as: x = P(odd) + P(red) - P(odd and red).

Statement 1: P(odd and red) = 0

Insufficient as we don't know P(odd) + P(red).

Statement 2: P(odd) - P(red) = 0.4

This can be true for various combination of P(odd) and P(red), for ex. P(odd)=0.5 and P(red)=0.1 or P(odd)=0.6 and P(red)=0.2 etc.

Hence, statement 2 is also insufficient!

Combining 1 and 2 also we do not have exact value of P(odd) and P(red). We just have values for P(odd)-P(red) and P(odd and red).

Therefore, the answer will be E.

--------------------------------------

P.S. Don't forget to give kudos

Quite not understood the logic
x = P(odd) + P(red) - P(odd and red).
1) says P(odd and red)=0
so x = P(odd) + P(red) - 0= x = P(odd) + P(red)

2) says
P(odd)- P(Red)=0.4
P(odd)= 0.5 so P(red)=0.1

combine 1 and 2

x= 0.5+0.1=0.6

are we not getting a value here?

Hi! RatneshS,

Statement 2 can have many combinations:-
P(odd)- P(Red)=0.4
P(odd)= 0.5 so P(red)=0.1
or P(odd)= 0.2 so P(red)=0.2 and so on.

We are not getting a unique value by combining both statement.
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Intern
Joined: 05 May 2017
Posts: 1
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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22 May 2017, 11:14
RatneshS wrote:
14101992 wrote:
For those of you who were not able to answer this, here is the answer.
We know there are cards written with numbers in different probability colours. We are asked for the probability of randomly selecting a card that has either an odd or is written in red. Let us assume this prob to be x.

So, x= (prob of selecting a card with an odd number) + (prob of selecting a card written in red) - (prob of selecting a card with an odd number written in red)
or we can write the above as: x = P(odd) + P(red) - P(odd and red).

Statement 1: P(odd and red) = 0

Insufficient as we don't know P(odd) + P(red).

Statement 2: P(odd) - P(red) = 0.4

This can be true for various combination of P(odd) and P(red), for ex. P(odd)=0.5 and P(red)=0.1 or P(odd)=0.6 and P(red)=0.2 etc.

Hence, statement 2 is also insufficient!

Combining 1 and 2 also we do not have exact value of P(odd) and P(red). We just have values for P(odd)-P(red) and P(odd and red).

Therefore, the answer will be E.

--------------------------------------

P.S. Don't forget to give kudos

Quite not understood the logic
x = P(odd) + P(red) - P(odd and red).
1) says P(odd and red)=0
so x = P(odd) + P(red) - 0= x = P(odd) + P(red)

2) says
P(odd)- P(Red)=0.4
P(odd)= 0.5 so P(red)=0.1

combine 1 and 2

x= 0.5+0.1=0.6

are we not getting a value here?

Hi! RatneshS,

Statement 2 can have many combinations:-
P(odd)- P(Red)=0.4
P(odd)= 0.5 so P(red)=0.1
or P(odd)= 0.2 so P(red)=0.2 and so on.

We are not getting a unique value by combining both statement.

Odd numbers between 1 and 20 is 10. So P(odd) = 10/50= 0.2
Am I doing something wrong?
Intern
Joined: 01 Jan 2018
Posts: 43
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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24 Apr 2018, 05:21
Hi,

Can someone explain this question in a simpler way? I'm sorry, I'm not able to understand the logic or correct me if I'm making some wrong assumptions.

Statement 1 says:

The probability that the card will both have an odd number and be written in red ink is 0.

Which means that the red cards are all even. Had there been one red card, which is odd then the probability wouldn't be 0.

So my understanding is that, all the red cards are even. So 10 cards.
then in the remaining 40 cards it'd be 20 blue cards of even and odd. 20 black cards of even and odd.

The probability of odd cards is 30/50 and probability of red card is 10/50.

So is the final answer 4/5? and is statement 1 not sufficient to answer?

Manager
Joined: 23 May 2017
Posts: 226
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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24 Apr 2018, 05:50
Each of the cards in a deck of 50 cards has a number from 1 to 20 written on it in either black, red or blue ink. If one card is to be selected at random from the deck, what is the probability that the card selected will either have an odd number or be written in red ink?

(1) The probability that the card will both have an off number and be written in red ink is 0.
P(O) . P(R) = 0

(2) The probability that the card will have an odd number minus the probability that the card will be written in red ink is 0.4
P(O) - P(R) = 0.4

Clearly 1 and 2 individually not sufficient.
combining both

P(O) - P(R) = 0.4 : Squaring both sides we get
$$[P(O)]^2$$ + $$[P(R)]^2$$ - 2$$P(O)$$.$$P(R)$$ = $$0.16$$ from statement 2 we know P(O).P(R) = 0

hence
$$[P(O)]^2$$ + $$[P(R)]^2$$ = $$0.16$$ = re-writing the LHS

$$[ P(O) + P(R) ]^2$$ -2$$P(O)$$.$$P(R)$$ = $$0.16$$

$$P(O).P(R) = 0$$ from statement 2

$$[ P(O) + P(R) ]^2$$ = $$0.16$$

$$[ P(O) + P(R) ]$$ = $$0.4$$ - which is a definite answer

What is wrong with my approach?
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Intern
Joined: 23 Jan 2017
Posts: 1
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20 [#permalink]

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07 May 2018, 23:30
14101992 wrote:
For those of you who were not able to answer this, here is the answer.
We know there are cards written with numbers in different probability colours. We are asked for the probability of randomly selecting a card that has either an odd or is written in red. Let us assume this prob to be x.

So, x= (prob of selecting a card with an odd number) + (prob of selecting a card written in red) - (prob of selecting a card with an odd number written in red)
or we can write the above as: x = P(odd) + P(red) - P(odd and red).

Statement 1: P(odd and red) = 0

Insufficient as we don't know P(odd) + P(red).

Statement 2: P(odd) - P(red) = 0.4

This can be true for various combination of P(odd) and P(red), for ex. P(odd)=0.5 and P(red)=0.1 or P(odd)=0.6 and P(red)=0.2 etc.

Hence, statement 2 is also insufficient!

Combining 1 and 2 also we do not have exact value of P(odd) and P(red). We just have values for P(odd)-P(red) and P(odd and red).

Therefore, the answer will be E.

--------------------------------------

P.S. Don't forget to give kudos

Correct me if I'm wrong:

P(odd) - P(red) = 0.4
squaring both sides:
[P(odd) - P(red)]^2 = 0.4^2
P(odd)^2 + P(red)^2 -2P(odd)xP(red) = 0.4^2
Since P(odd and red) = 0 (from statement 1): 2P(odd)xP(red) = 0
P(odd)^2 + P(red)^2 = 0.4^2

Now we have to calculate P(odd) + P(red)
squaring this expression we get:
P(odd)^2 + P(red)^2 + 2P(odd)xP(red)
Since P(odd and red) = 0 (from statement 1): 2P(odd)xP(red) = 0; we are left with
P(odd)^2 + P(red)^2
which we have proved above to be 0.4^2
Re: Each of the cards in a deck of 50 cards has a number from 1 to 20   [#permalink] 07 May 2018, 23:30
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# Each of the cards in a deck of 50 cards has a number from 1 to 20

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