Question

At a school carnival​ game, players toss beanbags onto a table with​ equal-sized squares of different colors. On the table there​ are:
8 green squares
5 orange squares
4 blue squares
Question content area bottom
Part 1
These statements describe the probabilities for different outcomes of a single beanbag toss that lands at a random location on the table. Select the number that best completes each statement.
The probability that the outcome is green is
A.0.471
0.471
B.0.294
0.294
C.0.667
0.667
D.0.235
0.235
The probability that the outcome is orange or green is
A.four seventeenths
four seventeenths
B.eight seventeenths
eight seventeenths

C.two thirds
two thirds
D.StartFraction 13 Over 17 EndFraction
StartFraction 13 Over 17 EndFraction
The probability that the outcome is not orange is
A.
23.5​%
B.
29.4​%
C.70.6
70.6
D.66.7
66.7

Answer 1

To find the probabilities, we first need to determine the total number of squares on the table. The total number of squares is the sum of the squares of each color:

- Green squares: 8
- Orange squares: 5
- Blue squares: 4

Total squares = \( 8 + 5 + 4 = 17 \)

Now, we can calculate the probabilities for each case.

### Part 1: The probability that the outcome is green

The probability of landing on a green square is calculated as:

\[
P(\text{Green}) = \frac{\text{Number of Green Squares}}{\text{Total Number of Squares}} = \frac{8}{17} \approx 0.471
\]

Thus, the correct answer is **A. 0.471**.

### Part 2: The probability that the outcome is orange or green

The probability of landing on either an orange square or a green square is calculated by adding their probabilities:

\[
P(\text{Orange or Green}) = P(\text{Orange}) + P(\text{Green}) = \frac{5}{17} + \frac{8}{17} = \frac{13}{17}
\]

Thus, the correct answer is **D. \(\frac{13}{17}\)**.

### Part 3: The probability that the outcome is not orange

To find the probability that the outcome is not orange, we can either calculate the complement of landing on an orange square or calculate directly.

First, let's find \( P(\text{Orange}) \):

\[
P(\text{Orange}) = \frac{5}{17}
\]

Thus, the probability of not landing on orange is:

\[
P(\text{Not Orange}) = 1 - P(\text{Orange}) = 1 - \frac{5}{17} = \frac{12}{17}
\]

To express this as a percentage:

\[
\frac{12}{17} \times 100 \approx 70.59\%
\]

Thus, the correct answer is **C. 70.6**.

### Summary of Answers:
1. The probability that the outcome is green: **A. 0.471**
2. The probability that the outcome is orange or green: **D. \(\frac{13}{17}\)**
3. The probability that the outcome is not orange: **C. 70.6**