Question

The data below shows the results of an experiment that was conducted by tossing a paper cup into the air and recording how it landed. If you were to toss the cup again, what is the probability (as a fraction) it would land upside down?

A 2 column table. The left column is labeled, How it Landed. The right column is labeled, frequency. Row 1: upside down, frequency 12. Row 2: on the side, frequency 30. Row 3: right side up, frequency 8.

Answer 1

To calculate the probability that the cup will land upside down, we first need to determine the total number of tosses. We can do this by adding the frequencies of all the different outcomes:

- Upside down: 12
- On the side: 30
- Right side up: 8

Now, we sum these frequencies:

\[
\text{Total tosses} = 12 + 30 + 8 = 50
\]

Next, we find the probability that the cup lands upside down. The probability is calculated using the formula:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case, the number of favorable outcomes (the cup landing upside down) is 12, and the total number of outcomes is 50. Thus, the probability \( P \) is:

\[
P(\text{upside down}) = \frac{12}{50}
\]

Now, we can simplify the fraction:

\[
P(\text{upside down}) = \frac{12 \div 2}{50 \div 2} = \frac{6}{25}
\]

Therefore, the probability that the cup would land upside down is \(\frac{6}{25}\).