Question

a six - sided die has its sides labeled with the numbers 1 to 6. what is the probability that, when rolled, the die lands on a side with a number less than 5? submit your answer as a simplified fraction, as well as a decimal and percentage, both rounded to the hundredths place. show your work here

Explanation:

Step1: Determine the total number of outcomes

A six - sided die has 6 possible outcomes. So, the total number of outcomes \(n = 6\).

Step2: Determine the number of favorable outcomes

The numbers less than 5 on a die are 1, 2, 3, 4. So, the number of favorable outcomes \(m=4\).

Step3: Calculate the probability as a fraction

The probability formula is \(P=\frac{m}{n}\). Substituting \(m = 4\) and \(n = 6\), we get \(P=\frac{4}{6}=\frac{2}{3}\).

Step4: Calculate the probability as a decimal

\(\frac{2}{3}=2\div3\approx0.67\) (rounded to the hundredths place).

Step5: Calculate the probability as a percentage

To convert the decimal to a percentage, we use the formula \(P(\text{percentage})=P(\text{decimal})\times100\). So, \(0.67\times100 = 67.00\%\).

Answer:

• Fraction: \(\frac{2}{3}\)
• Decimal: \(0.67\)
• Percentage: \(67.00\%\)