At a certain college, 30% of the students are from out of state. Find the probability that, if 8 students are randomly selected, 5 of them are from out of state.

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26-10-2022
Mathematics

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At a certain college, 30% of the students are from out of state. Find the probability that, if 8 students are randomly selected, 5 of them are from out of state.

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ShahdF672625 ShahdF672625 · Answer 1 · 2022-10-26T07:48:13+02:00

Percentage of students from out of state = 30%

If 8 students are selected, what is the probability that 5 are from out of state

The probability formula is given by:

[tex]\text{ P(E)=}\frac{\text{ n(Required outcome)}}{\text{ n(Total outcome)}}[/tex]

Hence,

[tex]\begin{gathered} P(5\text{ are from out of state, 30\%)=}\frac{5}{8}\text{ }\times30\text{ \%} \\ =\frac{5}{8}\times\frac{30}{100} \\ =\frac{3}{16} \end{gathered}[/tex]

Therefore, the probability that 5 of them are out of state is 3/16