Question

A kiddie pool holds miniature plastic ducks in different colors. Sophia randomly picks up a duck and then replaces it. She repeats this process 100 times. The table shows the results of her experiment.

Duck Color Times Picked
red 30
green 20
yellow 40
blue 10

What is the relative frequency of choosing a red duck? What color of duck is there likely to be the most of in the pool?

A.
The relative frequency is 0.3. It is likely that most ducks are blue.

B.
The relative frequency is 0.2. It is likely that most ducks are yellow.

C.
The relative frequency is 0.3. It is likely that most ducks are yellow.

D.
The relative frequency is 0.2. It is likely that most ducks are green.

Answer 1

.3 and most ducks are yellow - so letter c.

Explanation:

remember: the formula for relative frequency is f/n.

f = number of times data occurred for an observation (30 red ducks picked)

n - total frequencies (100 ducks picked in total)

30/100 = 0.3 is the relative frequency of choosing a red duck.

Next,

Yellow was picked 40 out of the 100 times, so its likely that most ducks are yellow.

Answer 2

C. The relative frequency is 0.3. It is likely that most ducks are yellow.

Explanation:

Relative frequency (or experimental probability) is calculated by dividing the recorded number of times an event happens by the total number of trials in the actual experiment.

`\begin{aligned}\implies \sf Relative\:frequency\:(red\:duck) & = \frac{\textsf{Number of times a red duck was picked}}{\textsf{Total number of trials}}\\\\ & = \sf (30)/(100)\\\\ & = \sf 0.3\end{aligned}`

The most likely color of duck in the pool is the color of duck with the highest frequency. Therefore, it is likely that most ducks are yellow.