Answer:0.277
Step-by-step explanation:
Given there are three boxes i.e. A , B and C
Probability of selecting any box is [tex]P_1=\frac{1}{3}[/tex]
Box A contains 2 keys out of which is 1 is correct so Probability of selecting the right key is [tex]P_2=\frac{1}{2}[/tex]
Box B contains 3 keys out of which is 1 is correct so Probability of selecting the right key is [tex]P_3=\frac{1}{3}[/tex]
Box C contains 2 keys out of which is 1 is correct but we cannot use it so Probability of selecting the right key is [tex]P_4=0[/tex]
Probability of selecting the right key is [tex]P=P_1\times P_2+P_1\times P_2+P_1\times P_3[/tex]
[tex]P=\frac{1}{3}\times \frac{1}{2}+\frac{1}{3}\times \frac{1}{3}+\frac{1}{3}\times 0[/tex]
[tex]P=\frac{5}{18}[/tex]
[tex]P=0.277[/tex]
