Question

A bag contains 77 orange marbles and 21 green marbles. If a representative sample contains 33 orange ​marbles, then how many green marbles would you expect it to​ contain? Explain. 100 points :)

Because the ratio of orange marbles to green marbles is ___ in the​ population, the expected number of green marbles is ___ times the number of orange marbles in the representative sample. There should be ___ green marbles.

Answer 1

9 green marbles are expected in the representative sample.

The expected number of green marbles is 0.27 times the number of orange marbles in the representative sample.

Explanation:

Given that,

• A bag contains 77 orange marbles and 21 green marbles.
• A representative sample contains 33 orange ​marbles and the green marbles not known.
• So, the expected number of green marbles can be assumed as 'x'.

The ratio of orange marbles to green marbles is in proportion to the ratio of orange marbles to green marbles in the representative sample.

To find the value of x :

The proportions are 77/21 = 33/x

Cross multiplying the denominators and keeping x alone on one side,

x = (33 × 21) ÷ 77

x = 693 ÷ 77

x = 9 green marbles.

Therefore, the number of green marbles expected in the representative sample is 9.

To find the how many times the green marbles is to the number of orange marbles in representative sample = 9/33 = 0.27 times.

The green marbles is 0.27 times to orange marbles in the representative sample.