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# A student applies to four colleges

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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 is given in 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 simplest form. College Probability Cardwell College 1/7 Broome College 1/8 Collaboration Institute 1/9 University of Sandwich 1/10

May 22, 2021

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Probabilty of none: $$\frac67 *\frac78 * \frac 89 * \frac{9}{10} = 0.6$$

So probabilty of at least 1 is 0.4 or 2/5

May 22, 2021