Manhattan Prep
A circus clown is entertaining kids by making balloon animals. The clown can make any one of the following animals: giraffe, dog, elephant, or monkey. The clown has five colors of balloons to choose from: red, yellow, blue, green, and purple. If the clown is just as likely to make any one of the animals and choose any one color, what is the probability that the clown will make a purple elephant?
A. 1/24
B. 1/20
C. 2/15
D. 3/20
E. 1/8
OA B
A circus clown is entertaining kids by making balloon
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As with many probability questions, we can solve this by using counting techniques or rules of probability.AAPL wrote:Manhattan Prep
A circus clown is entertaining kids by making balloon animals. The clown can make any one of the following animals: giraffe, dog, elephant, or monkey. The clown has five colors of balloons to choose from: red, yellow, blue, green, and purple. If the clown is just as likely to make any one of the animals and choose any one color, what is the probability that the clown will make a purple elephant?
A. 1/24
B. 1/20
C. 2/15
D. 3/20
E. 1/8
OA B
Let's use rules of probability
P(balloon animal is an elephant) = 1/4 [since there are 4 possible animals and 1 is an elephant]
P(balloon animal is purple) = 1/5 [since there are 5 possible colors and 1 is purple]
P(clown makes a purple elephant balloon animal) = P(balloon animal is elephant AND balloon animal is purple)
= P(balloon animal is elephant) x P(balloon animal is purple)
= 1/4 x 1/5
= 1/20
Answer: B
Cheers,
Brent
We can solve this problem as follows,
The probability of clown picking the purple balloon = 1/5
The probability of clown making an elephant = 1/4
The probability of clown making a purple elephant = 1/5 * 1/4 = 1/20
Regards!
The probability of clown picking the purple balloon = 1/5
The probability of clown making an elephant = 1/4
The probability of clown making a purple elephant = 1/5 * 1/4 = 1/20
Regards!
- fskilnik@GMATH
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$$\left\{ \matrix{AAPL wrote:Manhattan Prep
A circus clown is entertaining kids by making balloon animals. The clown can make any one of the following animals: giraffe, dog, elephant, or monkey. The clown has five colors of balloons to choose from: red, yellow, blue, green, and purple. If the clown is just as likely to make any one of the animals and choose any one color, what is the probability that the clown will make a purple elephant?
A. 1/24
B. 1/20
C. 2/15
D. 3/20
E. 1/8
\,4\,{\rm{animals}} \hfill \cr
\,5\,{\rm{colors}} \hfill \cr} \right.\,\,\,\,\, \to \,\,\,\,{\rm{randomly}}\,\,{\rm{choice}}\,\,{\rm{of}}\,\,{\rm{one}}\,\,{\rm{of}}\,\,{\rm{each}}$$
$${\rm{? = P}}\left( {\,{\rm{certain}}\,\,{\rm{animal}}\,\,{\rm{and}}\,\,{\rm{certain}}\,\,{\rm{color}}\,} \right)$$
$${\rm{Total}} = 4 \cdot 5 = 20\,\,\,{\rm{equiprobable}}\,\,{\rm{choices}}$$
$$? = {1 \over {20}}$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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The total number of different colored balloon animals can be made is 4 x 5 = 20. Thus, the probability that the clown will make a purple elephant is 1/20.AAPL wrote:Manhattan Prep
A circus clown is entertaining kids by making balloon animals. The clown can make any one of the following animals: giraffe, dog, elephant, or monkey. The clown has five colors of balloons to choose from: red, yellow, blue, green, and purple. If the clown is just as likely to make any one of the animals and choose any one color, what is the probability that the clown will make a purple elephant?
A. 1/24
B. 1/20
C. 2/15
D. 3/20
E. 1/8
Answer: B
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