Answer:
0.6494 or 64.94%
Step-by-step explanation:
In order for at least one trio to play on Friday night, at least one piano player (P), at least one guitar player (G) and at least one sax player (S) must show up.
The probabilities that at least one of each show up are:
[tex]P(P\geq 1) = 1-P(P=0)\\P(P\geq 1) = 1-\frac{100-77}{100}*\frac{100-77}{100} \\P(P\geq 1) =0.9471\\\\P(G\geq 1) = 1-P(G=0)\\P(G\geq 1) = 1-\frac{100-87}{100}*\frac{100-87}{100} \\P(G\geq 1) =0.9831\\\\P(S\geq 1) = 1-P(S=0)\\P(S\geq 1) = 1-\frac{100-45}{100}*\frac{100-45}{100} \\P(S\geq 1) =0.6975[/tex]
Therefore, the probability that at least one trio will play is:
[tex]P=P(P\geq 1)*P(G\geq 1)*P(S\geq 1) \\P=0.9471*0.9831*0.6975\\P=0.6494[/tex]
The probability is 0.6494 or 64.94%.
