When a certain computer plays 24-point game, each of Δ and

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When a certain computer plays 24-point game, each of Δ and @ representative operation of addition, subtraction, multiplication, and division. And each of the symbol has the following probability,

Δ -> +: 0.4 -:0.3×: 0.2 ÷: 0.1
@ -> +:0.6 -: 0.2 ×: 0.1 ÷: 0.1.

What is the probability if the computer calculates (4Δ2)(3@1)=24?

A. 0.28
B. 0.34
C. 0.44
D. 0.64
E. 0.84


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by Max@Math Revolution » Mon Feb 29, 2016 7:31 pm
When a certain computer plays 24-point game, each of Δ and @ representative operation of addition, subtraction, multiplication, and division. And each of the symbol has the following probability,

Δ -> +: 0.4 -:0.3×: 0.2 ÷: 0.1
@ -> +:0.6 -: 0.2 ×: 0.1 ÷: 0.1.

What is the probability if the computer calculates (4Δ2)(3@1)=24?

A. 0.28
B. 0.34
C. 0.44
D. 0.64
E. 0.84


-> The number of cases for (4Δ2)(3@1)=24 is
from Δ=× and @=× or ÷, (0.2)(0.1)+(0.2)(0.1)=0.04
and from Δ=+ and @=+, (0.4)(0.6)=0.24, which becomes 0.04+0.24=0.28.
Thus, A is the answer.