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In a jar there are 3 red balls and 2 blue balls. What is the

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LucyDang
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In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   31 Jul 2014, 06:47
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In a jar there are 3 red balls and 2 blue balls. What is the probability of drawing at least one red ball when drawing two consecutive balls randomly?

A. 9/10
B. 16/20
C. 2/5
D. 3/5
E. ½
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Bunuel
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   31 Jul 2014, 07:00
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LucyDang wrote:
In a jar there are 3 red balls and 2 blue balls. What is the probability of drawing at least one red ball when drawing two consecutive balls randomly?

A. 9/10
B. 16/20
C. 2/5
D. 3/5
E. ½


P(at least one red) = 1 - P(no red, so 2 blue) = 1- 2/5*1/4 = 9/10.

Answer: A.
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   31 Jul 2014, 07:01
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Bunuel wrote:
LucyDang wrote:
In a jar there are 3 red balls and 2 blue balls. What is the probability of drawing at least one red ball when drawing two consecutive balls randomly?

A. 9/10
B. 16/20
C. 2/5
D. 3/5
E. ½


P(at least one red) = 1 - P(no red, so 2 blue) = 1- 2/5*1/4 = 9/10.

Answer: A.


Some "at least" probability questions to practice:
leila-is-playing-a-carnival-game-in-which-she-is-given-140018.html
a-fair-coin-is-tossed-4-times-what-is-the-probability-of-131592.html
for-each-player-s-turn-in-a-certain-board-game-a-card-is-132074.html
a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html
a-shipment-of-8-tv-sets-contains-2-black-and-white-sets-and-53338.html
on-a-shelf-there-are-6-hardback-books-and-2-paperback-book-135122.html
in-a-group-with-800-people-136839.html
the-probability-of-a-man-hitting-a-bulls-eye-in-one-fire-is-136935.html
for-each-player-s-turn-in-a-certain-board-game-a-card-is-141790.html
the-probability-that-a-convenience-store-has-cans-of-iced-128689.html
triplets-adam-bruce-and-charlie-enter-a-triathlon-if-132688.html
a-manufacturer-is-using-glass-as-the-surface-144642.html
the-probability-is-1-2-that-a-certain-coin-will-turn-up-head-144730.html (OG13)
a-fair-coin-is-to-be-tossed-twice-and-an-integer-is-to-be-148779.html
in-a-game-one-player-throws-two-fair-six-sided-die-at-the-151956.html
in-a-drawer-of-shirts-8-are-blue-6-are-green-and-4-are-24418.html
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LucyDang
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   31 Jul 2014, 07:33
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Bunuel wrote:
Bunuel wrote:
LucyDang wrote:
In a jar there are 3 red balls and 2 blue balls. What is the probability of drawing at least one red ball when drawing two consecutive balls randomly?

A. 9/10
B. 16/20
C. 2/5
D. 3/5
E. ½


P(at least one red) = 1 - P(no red, so 2 blue) = 1- 2/5*1/4 = 9/10.

Answer: A.


Some "at least" probability questions to practice:
leila-is-playing-a-carnival-game-in-which-she-is-given-140018.html
a-fair-coin-is-tossed-4-times-what-is-the-probability-of-131592.html
for-each-player-s-turn-in-a-certain-board-game-a-card-is-132074.html
a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html
a-shipment-of-8-tv-sets-contains-2-black-and-white-sets-and-53338.html
on-a-shelf-there-are-6-hardback-books-and-2-paperback-book-135122.html
in-a-group-with-800-people-136839.html
the-probability-of-a-man-hitting-a-bulls-eye-in-one-fire-is-136935.html
for-each-player-s-turn-in-a-certain-board-game-a-card-is-141790.html
the-probability-that-a-convenience-store-has-cans-of-iced-128689.html
triplets-adam-bruce-and-charlie-enter-a-triathlon-if-132688.html
a-manufacturer-is-using-glass-as-the-surface-144642.html
the-probability-is-1-2-that-a-certain-coin-will-turn-up-head-144730.html (OG13)
a-fair-coin-is-to-be-tossed-twice-and-an-integer-is-to-be-148779.html
in-a-game-one-player-throws-two-fair-six-sided-die-at-the-151956.html
in-a-drawer-of-shirts-8-are-blue-6-are-green-and-4-are-24418.html


Hi Bunuel,

You're super fast!!! Many thanks to your resources! Indeed, I'm practicing probability right now, hihi..
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In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   31 Jul 2014, 20:40
Another way to solve this problem is:

P (at least 1 red) = 1 - P (no red)

\(P(H=2)=\frac{C^2_2}{C^2_5}=\frac{1}{10}\)

Hence, \(P({at least 1 red})=1-\frac{1}{10}=\frac{9}{10}\).
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   31 Jul 2014, 21:15
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P ( at least one red) = 1 - P ( all blue balls )

P( all blue balls ) = 2/5 ( for the first draw) * 1/4 ( for the second draw)
= 2/20 = 1/10

P ( at least one red ) = 1 - 1/10 = 9/10
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   05 Aug 2014, 18:57
I see that using \(P(at least 1 red)\) = \(1 - P(no red)\) is the quick way to solve this.

However, should \(P(at least 1 red) = P(1 red) + P(2 red)\) work?

where \(P(2 red) = \frac{3C2}{5C2}\) and \(P(1 red)= \frac{2(3C1*2C1)}{5C2}\)

Its not working ofcource because \(P(1 red)= \frac{2(3C1*2C1)}{5C2}\) is greater than 1. I multiplied by 2 because I think I have seen Bunuel solve such problems and account for the two ways of picking two balls i.e (B,R) or (R,B)

Where am I wrong in my thinking?

Thanks for the help
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   05 Aug 2014, 19:33
gooner wrote:
I see that using \(P(at least 1 red)\) = \(1 - P(no red)\) is the quick way to solve this.

However, should \(P(at least 1 red) = P(1 red) + P(2 red)\) work?

where \(P(2 red) = \frac{3C2}{5C2}\) and \(P(1 red)= \frac{2(3C1*2C1)}{5C2}\)

Its not working ofcource because \(P(1 red)= \frac{2(3C1*2C1)}{5C2}\) is greater than 1. I multiplied by 2 because I think I have seen Bunuel solve such problems and account for the two ways of picking two balls i.e (B,R) or (R,B)

Where am I wrong in my thinking?

Thanks for the help



Hi Gooner,

Here order of choosing Blue and Red do not matter. Hence do not multiply with 2.
\(P(1 red)= \frac{(3C1*2C1)}{5C2}\)
\(P(2 red)= \frac{(3C2)}{5C2}\)

Finally probability of choosing atleast one red is P(1 red) + p(2 red) = \(\frac{(3C1*2C1)}{5C2}\) + \(\frac{(3C2)}{5C2}\).

i.e., 3+6/10 = 9/10.
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In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   05 Aug 2014, 19:55
Sowmith wrote:
gooner wrote:
I see that using \(P(at least 1 red)\) = \(1 - P(no red)\) is the quick way to solve this.

However, should \(P(at least 1 red) = P(1 red) + P(2 red)\) work?

where \(P(2 red) = \frac{3C2}{5C2}\) and \(P(1 red)= \frac{2(3C1*2C1)}{5C2}\)

Its not working ofcource because \(P(1 red)= \frac{2(3C1*2C1)}{5C2}\) is greater than 1. I multiplied by 2 because I think I have seen Bunuel solve such problems and account for the two ways of picking two balls i.e (B,R) or (R,B)

Where am I wrong in my thinking?

Thanks for the help



Hi Gooner,

Here order of choosing Blue and Red do not matter. Hence do not multiply with 2.
\(P(1 red)= \frac{(3C1*2C1)}{5C2}\)
\(P(2 red)= \frac{(3C2)}{5C2}\)

Finally probability of choosing atleast one red is P(1 red) + p(2 red) = \(\frac{(3C1*2C1)}{5C2}\) + \(\frac{(3C2)}{5C2}\).

i.e., 3+6/10 = 9/10.


Thanks for that. I am trying to think of the scenario where I saw the solution account for the two ways of selecting the desired outcome.
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   13 Jul 2016, 03:55
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3 Red and 2 Blue balls

Balls taken out can be RR or RB

RR=Number of combinations=2!/2!
RB=Number of combinations=2!(RB or BR)

P(RB)+P(RR)=2*3/5*2/4+3/5*2/4=9/10
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   13 Jul 2016, 08:19
p(no red balls drawn)=2/5*1/4=1/10
p(at least 1 red)=1-1/10=9/10
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probability [#permalink] New post   09 Jul 2017, 17:47
In a jar there are 3 red balls and 2 blue balls. What is the probability og drawing at least one red ball when drawing two consecutive balls randomly.
A.9/10
B.16/20
C.2/5
D.3/5
E.1/2

Why are we considering this question to be without replacement ?? Can someone please explain under what conditions do we have to do so? Thank you
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Re: probability [#permalink] New post   09 Jul 2017, 19:00
longhaul123 wrote:
In a jar there are 3 red balls and 2 blue balls. What is the probability og drawing at least one red ball when drawing two consecutive balls randomly.
A.9/10
B.16/20
C.2/5
D.3/5
E.1/2

Why are we considering this question to be without replacement ?? Can someone please explain under what conditions do we have to do so? Thank you



Because he draws two consecutive balls randomly. therefore with replacement could not be considered...
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Re: probability [#permalink] New post   09 Jul 2017, 19:08
Usually if the ball is replaced it will either be mentioned specifically, or you will be given that the ball was drawn "one by one" or "one after another", instead of consecutively.
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   24 Nov 2019, 00:57
Bunuel wrote:
LucyDang wrote:
In a jar there are 3 red balls and 2 blue balls. What is the probability of drawing at least one red ball when drawing two consecutive balls randomly?

A. 9/10
B. 16/20
C. 2/5
D. 3/5
E. ½


P(at least one red) = 1 - P(no red, so 2 blue) = 1- 2/5*1/4 = 9/10.

Answer: A.


Bunuel

I understood that the best way to solve these "Atleast" problem is to find ( 1 - P) way.
But i proceeded by actually finding the Probabilities as given below:
Probability of drawing both red balls = 3/5 x 2/4 =6/20 = 3/10
Probability of drawing one red & one blue ball= 3/5 x 2/4 = 3/10 ( even if we draw blue ball first, the final value remains the same. = 2/5 x 3/4 =6/20 = 3/10)

Now adding both the probabilities, 3/10 + 3/10 = 2 x 3/10 = 6 /10 = 3/5 which is answer D

Can you tell where i went wrong.
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   24 Nov 2019, 02:04
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pandajee wrote:
Bunuel wrote:
LucyDang wrote:
In a jar there are 3 red balls and 2 blue balls. What is the probability of drawing at least one red ball when drawing two consecutive balls randomly?

A. 9/10
B. 16/20
C. 2/5
D. 3/5
E. ½


P(at least one red) = 1 - P(no red, so 2 blue) = 1- 2/5*1/4 = 9/10.

Answer: A.


Bunuel

I understood that the best way to solve these "Atleast" problem is to find ( 1 - P) way.
But i proceeded by actually finding the Probabilities as given below:
Probability of drawing both red balls = 3/5 x 2/4 =6/20 = 3/10
Probability of drawing one red & one blue ball= 3/5 x 2/4 = 3/10 ( even if we draw blue ball first, the final value remains the same. = 2/5 x 3/4 =6/20 = 3/10)

Now adding both the probabilities, 3/10 + 3/10 = 2 x 3/10 = 6 /10 = 3/5 which is answer D

Can you tell where i went wrong.


P(at least one red) = P(1 red, 1 blue) + P(2 red) = 3/5*2/4*2 + 3/5*2/4 = 9/10. You should multiply 3/5*2/4 by 2 because 1 red and 1 blue can occur in two ways: RB or BR.
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Re: In a jar there are 3 red balls and 2 blue balls. What is the [#permalink] New post   20 Feb 2022, 11:20
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