Question

The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. if there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female?

A) 0.410
B) 0.357
C) 0.333
D) 0.250


only those will answer you know otherwise reported on spot ​

Answer 1

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The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. if there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female?

A) 0.410

B) 0.357

C) 0.333

D) 0.250

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• Let x be the number of left-handed female students

• and Let y be the number of left-handed male students.

So,

The number of right-handed female students will be 5x and the number of right-handed male students will be 9y.

Since the total number of left-handed students is 18 and the total number of right-handed students is 122,

Then,

The system of equations below must be true:

x + y = 18

5x + 9y = 122

• When you solve this system of equations-

You get x = 10 and y = 8.

Thus, 5×10, or 50, of the 122 right-handed students are female.

Therefore, the probability that a right-handed student selected at random is female is

$\frac{50}{120}$

which to the nearest thousandth is 0.410.

• So, the final answer is option A.

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Answer 2

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Let x be the number of left-handed female students

and Let y be the number of left-handed male students.

So:-

The number of right-handed female students will be 5x and the number of right-handed male students will be 9y.

Since the total number of left-handed students is 18 and the total number of right-handed students is 122,

Then:-

The system of equations below must be true:

x + y = 18

5x + 9y = 122

When you solve this system of equations-

You get x = 10 and y = 8.

Thus,

5×10, or 50, of the 122 right-handed students are female.

So, the probability that a right-handed student selected at random is female is :-

$\begin{gathered} \frac{50}{120} \\ \end{gathered}$

which is the nearest thousandth is 0.410.

So, the answer is option A.