Question

Santiago got the board game Andromeda Aliens for his birthday. The game comes with a purple weighted die that is given as a reward to a player who captures an alien spaceship. To see how the die is​ weighted, Santiago rolls it 27 times and records the results.
Number on die
Times Rolled
1
4
2
10
3
2
4
6
5
4
6
1

Based on the​ data, what is the probability that the next roll of this die is a​ 5?
Write your answer as a fraction or whole number.
  
enter your response here
Write your answer as a decimal rounded to the nearest hundreths.
  
enter your response here

Answer 1

To find the probability of rolling a 5 with the die, we first need to determine the total number of times the die was rolled and how many times a 5 was rolled.

From the data provided, the counts for each face of the die are as follows:

- 1: 4 times
- 2: 10 times
- 3: 2 times
- 4: 6 times
- 5: 4 times
- 6: 1 time

Now, we calculate the total number of rolls:

\[
\text{Total Rolls} = 4 + 10 + 2 + 6 + 4 + 1 = 27
\]

Next, we find the number of times a 5 was rolled, which is 4.

Now we can calculate the probability \( P(5) \) of rolling a 5:

\[
P(5) = \frac{\text{Number of times 5 is rolled}}{\text{Total Rolls}} = \frac{4}{27}
\]

### Fraction
The probability that the next roll of this die is a 5 is:

\[
\frac{4}{27}
\]

### Decimal
Now let's convert this fraction into a decimal. We can calculate:

\[
\frac{4}{27} \approx 0.148148
\]

Rounding this to the nearest hundredth:

\[
\approx 0.15
\]

### Summary:
- As a fraction: \(\frac{4}{27}\)
- As a decimal (rounded to the nearest hundredth): \(0.15\)