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Answer:
The value of P (A) is 0.00833.
The value of P (B) is 0.00139.
Step-by-step explanation:
It is provided that there are 10 acts on a talent show.
The two events are defined as follows:
A: First three acts dancer, singer and the guitarist in any order
B: The comedian first guitarist second and pianist third
(1)
Compute the number of ways to select 3 acts from the 10 as follows:
There are 120 ways to select 3 acts from the 10 and only 1 way to select a dancer, singer and the guitarist in any order.
Compute the probability of selecting a dancer, singer and the guitarist in any order as follows:
Thus, the value of P (A) is 0.00833.
(2)
Compute the number of ways to select 3 acts from the 10 (without replacement) and with order as follows:
There are 720 ways to select 3 acts from the 10 with order and only 1 way to select the comedian first guitarist second and pianist third.
Compute the probability of selecting the comedian first guitarist second and pianist third as follows:
Thus, the value of P (B) is 0.00139.