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 8 equal - sized sectors. The total number of possible outcomes when spinning the spinner is $n = 8$. The number of black sectors (favorable outcomes) is $m=3$.

Step2: Calculate probability as a fraction

The probability $P$ of an event is given by the formula $P=\frac{m}{n}$. So, $P=\frac{3}{8}$.

Step3: Convert fraction to decimal

To convert $\frac{3}{8}$ to a decimal, we divide 3 by 8: $3\div8 = 0.375\approx0.38$.

Step4: Convert decimal to percentage

To convert the decimal to a percentage, we multiply by 100. So, $0.375\times100 = 37.5\%\approx38\%$.

Answer:

Fraction: $\frac{3}{8}$
Decimal: $0.38$
Percent: $38\%$