X~Bin(2,1/3), while Y+Z~Poisson(3), independently. Favorable cases are X=1 with Y+Z=0, or X=2 with Y+Z≤1. Probability=(4/9)e⁻³+(1/9)(1+3)e⁻³=(8/9)e⁻³. Multiply by 10 to obtain **.44**.
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