Answered

Find answers to your questions and expand your knowledge with IDNLearn.com. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.

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]

Sagot :

GinnyAnsweridn
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].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.