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A student applies to four colleges, all of which decide admissions through random lotteries. The probability of admissions to each college in given int the table below. If the student applies to all four of these colleges, what is the probability that he is admitted to at least one of them? Express your answer as a fraction in the simplest form. Table: Cardwell College: 1/7 Broome College: 1/8 Collaboration Institute: 1/9 University of sandwich: 1/10 (This is a real question, please help)

 Jun 5, 2021
 #1
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The probability of being admitted to at least one college is  1 - (probability of not being admitted to any)

 

Carwell College:                admitted = 1/7      not admitted = 6/7

Broome College:               admitted = 1/8       not admitted = 7/8

Collaboration Institute:      admitted = 1/9       not admitted = 8/9

University of Sandwich:     admitted = 1/10     not admitted = 9/10

 

Probability of not being admitted to any:  (6/7) · (7/8) · (8/9) · (9/10)

 

Find the answer to that multiplication problem and then subtract that answer from 1.

 Jun 5, 2021
 #2
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so then it would be 0.4? 

Guest Jun 5, 2021
 #3
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so it would be 0.4 so there for he has a 40% chance of entering?

Guest Jun 5, 2021

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