Math / Data & Statistics

Question2. Sophia tests 25 pens. Five of the pens do not write the first time. Sophia says the experimental probability that a pen will not write the first time is 0.2 . Is Sophia correct? Why? a. No, because you cannot predict whether the next pen will write or not b. No, because $\frac{20}{25}$ is 0.8 c. Yes, because $\frac{20}{25}$ is 0.2 d.) Yes, because $\frac{5}{25}$ is 0.2

Studdy Solution

STEP 1

1. Sophia tested a total of 25 pens.
2. Out of these, 5 pens did not write the first time.
3. Experimental probability is calculated as the ratio of the number of successful outcomes to the total number of trials.

STEP 2

1. Calculate the experimental probability.
2. Compare the calculated probability with Sophia's claim.
3. Determine the correctness of Sophia's statement and choose the appropriate option.

STEP 3

Calculate the experimental probability that a pen will not write the first time. This is given by the ratio of the number of pens that did not write to the total number of pens tested:
$\text{Experimental Probability} = \frac{\text{Number of pens that did not write}}{\text{Total number of pens}} = \frac{5}{25}$

STEP 4

Simplify the fraction $\frac{5}{25}$ :
$\frac{5}{25} = \frac{1}{5} = 0.2$

STEP 5

Compare the calculated probability (0.2) with Sophia's claim (0.2). Since they are equal, Sophia's statement is correct.
The correct option is:
$\text{d.) Yes, because } \frac{5}{25} \text{ is 0.2}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms