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# One box contains 30 purple balls and 20 red balls, another box contain

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Math Expert
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Re: One box contains 30 purple balls and 20 red balls, another box contain [#permalink]
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Bunuel wrote:
One box contains 30 purple balls and 20 red balls, another box contains 15 purple balls and 35 red balls, if Wendy randomly chooses one box and draws one ball from it, what will be the possibility that the ball will be purple?

A. 3/10
B. 3/20
C. 9/10
D. 9/20
E. 7/20

There are two ways to win:
(1) Choose box 1 AND choose purple.
OR
(2) Choose box 2 AND choose purple.

AND means multiply. OR means add.

(1)
Probability of choosing box 1 = 0.5
Probability of choosing purple = 30/50 = 0.6
Probability of choosing box 1 AND choosing purple = 0.5*0.6 = 0.3

(2)
Probability of choosing box 2 = 0.5
Probability of choosing purple = 15/50 = 0.3
Probability of choosing box 2 AND choosing purple = 0.5*0.3 = 0.15

Probability of (1) OR (2) = 0.3+0.15 = 0.45 = 9/20

.
.
.

Bonus credit if you spotted that we didn't need to do all of that because the probability of choosing box 1 equals the probability of choosing box 2. If you did spot that, you're probably not reading this. If you didn't spot it, don't worry about it, since GMAC doesn't give two hoots how you get to the right answer!!
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Re: One box contains 30 purple balls and 20 red balls, another box contain [#permalink]
Please correct me if my way of thinking is completely wrong.

Box 1 = 30 Purple + 20 Red
Box 1 = 15 Purple + 35 Red

Combined = 45 Purple + 55 Red

Question ask for the possibility of drawing a purple ball, which must be just under 50% therefore 9/20

Hope it helps
Tutor
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Re: One box contains 30 purple balls and 20 red balls, another box contain [#permalink]
ChrestenB wrote:
Please correct me if my way of thinking is completely wrong.

Box 1 = 30 Purple + 20 Red
Box 1 = 15 Purple + 35 Red

Combined = 45 Purple + 55 Red

Question ask for the possibility of drawing a purple ball, which must be just under 50% therefore 9/20

Hope it helps

That's a-okay in this case. Would it work if the probability of choosing box 1 is 40% and the probability of choosing box 2 is 60%? What adjustment would you need to make to your approach in that case?
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Re: One box contains 30 purple balls and 20 red balls, another box contain [#permalink]
P(Purple) = P(purple1)+P(Purple2)

P(purple1) = 1/2 X 3/5 = 3/10 ( P choosing bag = 1/2 + P choosing purple from bag 1 = 30/50)
P(purple2) = 1/2 X 15/50 =15/100

P(Purple) = 3/10 + 15/100 = 9/20 Option "D"
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One box contains 30 purple balls and 20 red balls, another box contain [#permalink]
Many people are doing wrong

The concept to learn is, probability of a AND b = p(a)*p(b)
Probability of a OR b is p(a) +p(b)

The ball drawn is purple from either of the bags (OR probability)

Therefore probability of selecting a bag is 1/2

Also, probability of drawing a purple ball

1/2(30/50 +15/20) = 9/20

Ans D

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One box contains 30 purple balls and 20 red balls, another box contain [#permalink]
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Math Expert
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