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2 years ago

13

A history test has 30 questions. A student answers 90% of the questions correctly. How many questions did the student get correc

t.

1 answer:

algol132 years ago

7 0

Answer:

27 questions

Step-by-step explanation:

Hope this helps!

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A group of three undergraduate and five graduate students are available to fill certain student government posts. If four studen

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Answer:

$Pr = 0.4286$

Step-by-step explanation:

Given

Let

$U \to\\$ Undergraduates

$G \to$ Graduates

So, we have:

$U = 3; G =5$ -- Total students

$r = 4$ --- students to select

Required

$P(U =2)$

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.

First, we calculate the total possible selection (using combination)

$^nC_r = \frac{n!}{(n-r)!r!}$

So, we have:

$Total = ^{U + G}C_r$

$Total = ^{3 + 5}C_4$

$Total = ^8C_4$

$Total = \frac{8!}{(8-4)!4!}$

$Total = \frac{8!}{4!4!}$

Using a calculator, we have:

$Total = 70$

The number of ways of selecting 2 from 3 undergraduates is:

$U = ^3C_2$

$U = \frac{3!}{(3-2)!2!}$

$U = \frac{3!}{1!2!}$

$U = 3$

The number of ways of selecting 2 from 5 graduates is:

$G = ^5C_2$

$G = \frac{5!}{(5-2)!2!}$

$G = \frac{5!}{3!2!}$

$G =10$

So, the probability is:

$Pr = \frac{G * U}{Total}$

$Pr = \frac{10*3}{70}$

$Pr = \frac{30}{70}$

$Pr = 0.4286$

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