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Claire estimates her chances of being admitted to her top five schools

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Claire estimates her chances of being admitted to her top five schools  [#permalink]

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New post 28 Feb 2019, 00:25
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E

Difficulty:

  85% (hard)

Question Stats:

42% (02:24) correct 58% (02:18) wrong based on 66 sessions

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Claire estimates her chances of being admitted to her top five schools as follows: 80 percent for Debs U, 70 percent for Powderly State, 50 percent for Randolph A&M, 20 percent for Reuther, and 10 percent for Chavez Poly. If Claire’s estimates are correct, her chance of being admitted to at least one of her top five schools is between

A. 75% and 79.99%
B. 80% and 84.99%
C. 85% and 89.99%
D. 90% and 94.99%
E. 95% and 99.99%

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Re: Claire estimates her chances of being admitted to her top five schools  [#permalink]

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New post 28 Feb 2019, 07:08
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Bunuel wrote:
Claire estimates her chances of being admitted to her top five schools as follows: 80 percent for Debs U, 70 percent for Powderly State, 50 percent for Randolph A&M, 20 percent for Reuther, and 10 percent for Chavez Poly. If Claire’s estimates are correct, her chance of being admitted to at least one of her top five schools is between

A. 75% and 79.99%
B. 80% and 84.99%
C. 85% and 89.99%
D. 90% and 94.99%
E. 95% and 99.99%


P of not getting into school
.2*.3*.5*.2*.9 = 0.021
1-0.021 = .97 ~ 97%
IMO E
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Re: Claire estimates her chances of being admitted to her top five schools  [#permalink]

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New post 28 Feb 2019, 14:52
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1
Bunuel wrote:
Claire estimates her chances of being admitted to her top five schools as follows: 80 percent for Debs U, 70 percent for Powderly State, 50 percent for Randolph A&M, 20 percent for Reuther, and 10 percent for Chavez Poly. If Claire’s estimates are correct, her chance of being admitted to at least one of her top five schools is between

A. 75% and 79.99%
B. 80% and 84.99%
C. 85% and 89.99%
D. 90% and 94.99%
E. 95% and 99.99%



80 percent for Debs U=> Fail Debs U = 20%
70 percent for Powderly State => Fail Powderly = 30%
50 percent for Randolph A&M => Fail Randolph = 50%
20 percent for Reuther => Fail Reu = 80%
10 percent for Chavez Poly => Fail Chavez = 90%

=> Chance of Fail all of 5 schools = 0.2*0.3*0.5*0.8*0.9 = 0.0216
=> Chance of getting at least 1 of 5 schools = 1 - 0.0216 = 0.9784 = 97.84%. Hence E
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Re: Claire estimates her chances of being admitted to her top five schools  [#permalink]

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New post 04 Mar 2019, 20:07
Bunuel wrote:
Claire estimates her chances of being admitted to her top five schools as follows: 80 percent for Debs U, 70 percent for Powderly State, 50 percent for Randolph A&M, 20 percent for Reuther, and 10 percent for Chavez Poly. If Claire’s estimates are correct, her chance of being admitted to at least one of her top five schools is between

A. 75% and 79.99%
B. 80% and 84.99%
C. 85% and 89.99%
D. 90% and 94.99%
E. 95% and 99.99%



We can use the formula:

P(being accepted to at least 1 school) = 1 - P(not being accepted to any schools)

P(not being accepted to any schools) = 0.2 x 0.3 x 0.5 x 0.8 x 0.9 = 0.0216

So the probability of being accepted to at least one school is 1 - 0.0216 = 0.9784.

Answer: E
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Re: Claire estimates her chances of being admitted to her top five schools   [#permalink] 04 Mar 2019, 20:07
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