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# Each of the 25 balls in a certain box is either red, blue or

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Joined: 19 Aug 2016
Posts: 73
Re: Each of the 25 balls in a certain box is either red, blue or [#permalink]

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26 Nov 2017, 19:33
Bunuel wrote:
Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

Probability ball: white - $$P(W)$$;
Probability ball: even - $$P(E)$$;
Probability ball: white and even - $$P(W&E)$$.

Probability ball picked being white or even: $$P(WorE)=P(W)+P(E)-P(W&E)$$.

(1) The probability that the ball will both be white and have an even number painted on it is 0 --> $$P(W&E)=0$$ (no white ball with even number) --> $$P(WorE)=P(W)+P(E)-0$$. Not sufficient

(2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2 --> $$P(W)-P(E)=0.2$$, multiple values are possible for $$P(W)$$ and $$P(E)$$ (0.6 and 0.4 OR 0.4 and 0.2). Can not determine $$P(WorE)$$.
)
(1)+(2) $$P(W&E)=0$$ and $$P(W)-P(E)=0.2$$ --> $$P(WorE)=2P(E)+0.2$$ --> multiple answers are possible, for instance: if $$P(E)=0.4$$ (10 even balls) then $$P(WorE)=1$$ BUT if $$P(E)=0.2$$ (5 even balls) then $$P(WorE)=0.6$$. Not sufficient.

Hope it's clear.

Hi Bunuel..

How did u get Probability ball picked being white or even: P(W or E)=P(W)+P(E)-P(W&E)?
Math Expert
Joined: 02 Sep 2009
Posts: 44399
Re: Each of the 25 balls in a certain box is either red, blue or [#permalink]

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26 Nov 2017, 21:06
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KUDOS
Expert's post
zanaik89 wrote:
Bunuel wrote:
Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

Probability ball: white - $$P(W)$$;
Probability ball: even - $$P(E)$$;
Probability ball: white and even - $$P(W&E)$$.

Probability ball picked being white or even: $$P(WorE)=P(W)+P(E)-P(W&E)$$.

(1) The probability that the ball will both be white and have an even number painted on it is 0 --> $$P(W&E)=0$$ (no white ball with even number) --> $$P(WorE)=P(W)+P(E)-0$$. Not sufficient

(2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2 --> $$P(W)-P(E)=0.2$$, multiple values are possible for $$P(W)$$ and $$P(E)$$ (0.6 and 0.4 OR 0.4 and 0.2). Can not determine $$P(WorE)$$.
)
(1)+(2) $$P(W&E)=0$$ and $$P(W)-P(E)=0.2$$ --> $$P(WorE)=2P(E)+0.2$$ --> multiple answers are possible, for instance: if $$P(E)=0.4$$ (10 even balls) then $$P(WorE)=1$$ BUT if $$P(E)=0.2$$ (5 even balls) then $$P(WorE)=0.6$$. Not sufficient.

Hope it's clear.

Hi Bunuel..

How did u get Probability ball picked being white or even: P(W or E)=P(W)+P(E)-P(W&E)?

OR probability:
If Events A and B are independent, the probability that Event A OR Event B occurs is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur: $$P(A \ or \ B) = P(A) + P(B) - P(A \ and \ B)$$.

This is basically the same as 2 overlapping sets formula:
{total # of items in groups A or B} = {# of items in group A} + {# of items in group B} - {# of items in A and B}.

Note that if event are mutually exclusive then $$P(A \ and \ B)=0$$ and the formula simplifies to: $$P(A \ or \ B) = P(A) + P(B)$$.

Also note that when we say "A or B occurs" we include three possibilities:
A occurs and B does not occur;
B occurs and A does not occur;
Both A and B occur.

AND probability:
When two events are independent, the probability of both occurring is the product of the probabilities of the individual events: $$P(A \ and \ B) = P(A)*P(B)$$.

This is basically the same as Principle of Multiplication: if one event can occur in $$m$$ ways and a second can occur independently of the first in $$n$$ ways, then the two events can occur in $$mn$$ ways.

22. Probability

For more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Joined: 24 Oct 2017
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Re: Each of the 25 balls in a certain box is either red, blue or [#permalink]

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04 Feb 2018, 13:33
Can someone tell me where my logic went wrong? I selected A, with the thought that since P(W&E)=0, therefore there must be 5 white balls, all of which have an odd number on them (so 5 white balls total). Therefore, P(W)=5/25, P(E)=10/25, and P(W&E)=0. Is it wrong to assume that the numbers don't repeat on each ball color (i.e. the blue balls with all of 1 number cannot be true?).
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Posts: 896
Location: India
Re: Each of the 25 balls in a certain box is either red, blue or [#permalink]

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04 Feb 2018, 22:57
ulanky wrote:
Can someone tell me where my logic went wrong? I selected A, with the thought that since P(W&E)=0, therefore there must be 5 white balls, all of which have an odd number on them (so 5 white balls total). Therefore, P(W)=5/25, P(E)=10/25, and P(W&E)=0. Is it wrong to assume that the numbers don't repeat on each ball color (i.e. the blue balls with all of 1 number cannot be true?).

Hi

P(W&E) = 0, means that there is NO ball which is both white and has an even number on it. But there could be various white balls with odd numbers on them, and there could be various red/blue balls with even numbers on them. We need to take both these kinds of balls into account.

I think we cannot assume that there must be 5 white balls, its possible that there is only one white ball in the entire box. And yes, I think we also cannot assume that the numbers cannot repeat on same coloured balls (because its nowhere given). Its possible that all blue coloured balls have only number 1 painted on them.
Re: Each of the 25 balls in a certain box is either red, blue or   [#permalink] 04 Feb 2018, 22:57

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