The winners of a carnival game draw a token from a box to determine their prize. Each winner draws a token and places it back into the box before the next draw. Every winner has a [tex]$25\%$[/tex] chance of getting a stuffed animal, a [tex]$26\%$[/tex] chance of getting a hat, and a [tex]$49\%$[/tex] chance of getting a basketball.

The game operator wants to simulate what could happen for the next ten winners. So for each winner, he generates a random whole number from 1 to 100.

(a) What is the range of values that the game operator can use to represent a winner getting a basketball?
[tex]$\square$[/tex] to [tex]$\square$[/tex]

(b) Here’s the game operator’s simulation:
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline
Winner & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
Random number & 30 & 86 & 59 & 24 & 68 & 74 & 15 & 50 & 32 & 66 \\
\hline
\end{tabular}
\][/tex]

Using your answer in part (a), find the percentage of the 10 simulated winners who got a basketball.
[tex]$\square \%$[/tex]

Question

08-08-2024
Mathematics

Answered

The winners of a carnival game draw a token from a box to determine their prize. Each winner draws a token and places it back into the box before the next draw. Every winner has a [tex]$25\%$[/tex] chance of getting a stuffed animal, a [tex]$26\%$[/tex] chance of getting a hat, and a [tex]$49\%$[/tex] chance of getting a basketball.

The game operator wants to simulate what could happen for the next ten winners. So for each winner, he generates a random whole number from 1 to 100.

(a) What is the range of values that the game operator can use to represent a winner getting a basketball?
[tex]$\square$[/tex] to [tex]$\square$[/tex]

(b) Here’s the game operator’s simulation:
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline
Winner & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
Random number & 30 & 86 & 59 & 24 & 68 & 74 & 15 & 50 & 32 & 66 \\
\hline
\end{tabular}
\][/tex]

Using your answer in part (a), find the percentage of the 10 simulated winners who got a basketball.
[tex]$\square \%$[/tex]

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-08-08T16:06:50-04:00

Let's solve the problem step by step:

### Part (a)

First, we need to determine the ranges of values that represent each prize based on the given percentages:
- A 25% chance of getting a stuffed animal means numbers from 1 to 25.
- A 26% chance of getting a hat means numbers from 26 to 51.
- A 49% chance of getting a basketball means numbers from 52 to 100.

To answer part (a):
The range of values for getting a basketball is from 52 to 100.

### Part (b)

Next, we use the given random numbers to determine the percentage of winners who got a basketball. The table provides the following random numbers drawn by the winners:

Random numbers: 30, 86, 59, 24, 68, 74, 15, 50, 32, 66

We need to identify which of these numbers fall within the basketball range (52 to 100):

- Random number 30: Not within the range (stuffed animal)
- Random number 86: Within the range (basketball)
- Random number 59: Within the range (basketball)
- Random number 24: Not within the range (stuffed animal)
- Random number 68: Within the range (basketball)
- Random number 74: Within the range (basketball)
- Random number 15: Not within the range (stuffed animal)
- Random number 50: Not within the range (hat)
- Random number 32: Not within the range (hat)
- Random number 66: Within the range (basketball)

Counting the numbers that fall within the basketball range, we find there are 5 numbers (86, 59, 68, 74, 66).

Now, to calculate the percentage of winners who got a basketball, we use the following formula:
[tex]\[ \text{{Percentage}} = \left( \frac{{\text{{Number of basketball winners}}}}{{\text{{Total number of winners}}}} \right) \times 100 \][/tex]

Plugging in the values:
[tex]\[ \text{{Percentage}} = \left( \frac{5}{10} \right) \times 100 = 50\% \][/tex]

To answer part (b):
The percentage of the 10 simulated winners who got a basketball is [tex]$50\%$[/tex].