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 35 times and records the results.
Number on die
Times Rolled
1
6
2
5
3
3
4
4
5
7
6
10

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 calculate the probability of rolling a 5 on Santiago's weighted die, we need to determine the total number of times a 5 was rolled and divide that by the total number of rolls.

From the data provided:

- The number 5 was rolled 7 times.
- The total number of rolls is 35.

Now, we can calculate the probability:

\[
P(5) = \frac{\text{Number of times 5 is rolled}}{\text{Total number of rolls}} = \frac{7}{35}
\]

Now, we simplify the fraction:

\[
P(5) = \frac{7 \div 7}{35 \div 7} = \frac{1}{5}
\]

So, the probability as a fraction is:

\[
\frac{1}{5}
\]

Now, to convert this probability to a decimal, we perform the division:

\[
P(5) = \frac{1}{5} = 0.2
\]

Rounded to the nearest hundredth, this is:

\[
0.20
\]

Thus, the final answers are:

1. As a fraction: \(\frac{1}{5}\)
2. As a decimal (rounded to two decimal places): \(0.20\)