Question

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?

Answer 1

There are 4 instrumentalist, 10 singers and 6 dancers.

Total number of participant = 20

Since There are random selection each talent type can occur with probability

$P(1)=P(2)=P(3)=\dfrac{1}{3}$

Probability of selecting the instrumentalist

$P(I)=\dfrac{4}{20}=\dfrac{1}{5}$

Probability of selecting the Singers

$P(S)=\dfrac{10}{20}=\dfrac{1}{2}$

Probability of selecting the Dancers

$P(D)=\dfrac{6}{20}=\dfrac{3}{10}$

Probability that Dancer performs first=$\dfrac{P(1).P(D)}{P(1).P(D)+P(2).P(I)+P(3).P(D)}$

$=\dfrac{\dfrac{1}{3}.\dfrac{3}{10}}{\dfrac{1}{3}.\dfrac{3}{10}+\dfrac{1}{3}.\dfrac{1}{5}+\dfrac{1}{3}.\dfrac{1}{2}}$

$=\dfrac{3}{10}=0 .3$ .