Question

the frequency table shows the results of tossing a number cube 50 times. which statement is reasonable, based on the data?
top number on cube frequency
1 8
2 10
3 6
4 10
5 7
6 9
the number 2 will be the next number tossed.
the probability of tossing the number 2 is 1/10.
the number 4 is half as likely to be tossed as the number 3.
tossing an even number is more likely than tossing an odd number.

Explanation:

Step1: Calculate probability of each number

Probability of a number = $\frac{\text{Frequency of the number}}{\text{Total number of tosses}}$. Total number of tosses = 50.
Probability of 1: $\frac{8}{50}=\frac{4}{25}$, Probability of 2: $\frac{10}{50}=\frac{1}{5}$, Probability of 3: $\frac{10}{50}=\frac{1}{5}$, Probability of 4: $\frac{6}{50}=\frac{3}{25}$, Probability of 5: $\frac{10}{50}=\frac{1}{5}$, Probability of 6: $\frac{9}{50}$.

Step2: Analyze each statement

• "The number 2 will be the next number tossed." - Each toss is independent, we can't predict the next number, so this is wrong.
• "The probability of tossing the number 2 is $\frac{1}{10}$." - Probability of 2 is $\frac{1}{5}$, so this is wrong.
• "The number 4 is half as likely to be tossed as the number 3." - Probability of 3 is $\frac{1}{5}=\frac{5}{25}$ and probability of 4 is $\frac{3}{25}$, $\frac{3}{25}$ is not half of $\frac{5}{25}$, so this is wrong.
• "Tossing an even number is more likely than tossing an odd number." - Even numbers: 2, 4, 6 with frequencies 10 + 6+ 9 = 25. Odd numbers: 1, 3, 5 with frequencies 8 + 10+ 10 = 28. Tossing an odd number is more likely, so this is wrong. But if we calculate probabilities: Probability of even = $\frac{25}{50}=\frac{1}{2}$, Probability of odd = $\frac{28}{50}=\frac{14}{25}$, $\frac{14}{25}>\frac{1}{2}$, still wrong.

Answer:

None of the statements are reasonable.