Question

question 13 · 1 point
the acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers. if the acts are ordered randomly, what is the probability that a dancer performs first?
provide the answer as a simplified fraction.
provide your answer below:

Explanation:

Step1: Calculate total number of acts

Total acts = Instrumentalists + Singers + Dancers = \(4 + 10 + 6 = 20\)

Step2: Calculate probability a dancer performs first

Number of dancers = 6. Probability = \(\frac{\text{Number of dancers}}{\text{Total number of acts}} = \frac{6}{20}\)

Step3: Simplify the fraction

Simplify \(\frac{6}{20}\) by dividing numerator and denominator by their GCD (2). \(\frac{6\div2}{20\div2} = \frac{3}{10}\)

Answer:

\(\frac{3}{10}\)