Question

a study conducted at a certain college shows that 55% of the schools graduates find a job in their chosen field within a year after graduation find the probability that amount 7 randomly selected graduates at least one finds a job in his or her chosen field withing a year of graduating​

Answer 1

The probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating​ is 0.9963, if a study conducted at a certain college showed that 55% of the schools graduates find a job in their chosen field within a year after graduation.

As mentioned in the question statement, a study conducted at a certain college shows that 55% of the schools graduates find a job in their chosen field within a year after graduation.

Therefore, probability of finding a job in their chosen field within a year after graduation, P(Finding a job) = $\frac{55}{100}=0.55$.

Then, probability of not finding a job in their chosen field within a year after graduation, P(Not finding a job) = [1 - P(Finding a job)] $=(1-0.55)=0.45$.

Therefore, probability that no one finds a job among seven random people = [ {P(Not finding a job)} ^ 7] = $(0.45)^{7} = 0.0037$.

Finally, probability that at least one finds a job among seven random people = [1 - {P(Not finding a job) ^ 7}] = $(1-0.0037)=0.9963$.

Hence, The probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating​ is 0.9963, if a study conducted at a certain college showed that 55% of the schools graduates find a job in their chosen field within a year after graduation.

• Probability: In mathematics, probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

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