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 fraction: decimal: percent

Explanation:

Step1: Determine the total number of outcomes

A six - sided die has \(n(S)=6\) possible outcomes (\(1,2,3,4,5,6\)).

Step2: Determine the number of favorable outcomes

The numbers less than \(5\) are \(1,2,3,4\). So \(n(E) = 4\).

Step3: Calculate the probability as a fraction

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting the values, we get \(P(E)=\frac{4}{6}=\frac{2}{3}\).

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, multiply by \(100\). So \(0.67\times100 = 67.00\%\).

Answer:

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