Question

a group of friends are playing a game using the following spinner. each of the colored sectors are the same size. if one of the friends takes a spin, what is the probability that the spinner will land on a black sector? submit your answer as a simplified fraction, as well as a decimal and percentage, both rounded to the hundredths place.

Explanation:

Step1: Determine total and favorable outcomes

The spinner is divided into 5 equal - sized sectors. The total number of possible outcomes when spinning the spinner is 5. The number of black sectors (favorable outcomes) is 3.

Step2: Calculate the probability as a fraction

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability as a fraction is $\frac{3}{5}$.

Step3: Convert the fraction to a decimal

To convert $\frac{3}{5}$ to a decimal, we divide 3 by 5: $3\div5 = 0.60$.

Step4: Convert the decimal to a percentage

To convert a decimal to a percentage, we multiply by 100. So $0.60\times100 = 60.00\%$.

Answer:

Fraction: $\frac{3}{5}$
Decimal: $0.60$
Percent: $60.00\%$