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Recruitment probability problem

P(ξ=0)=( 1- 13)? ( 1-p)= 12,

∴ 1-p=34,∴p= 14,

The possible values of ξ are 0, 1 2,

P(ξ=0)= 12,

P(ξ= 1)= 13×( 1? 14)+( 1? 13)× 14=5 12,

p(ξ= 2)= 13× 14 = 1 12,

∴eξ=0× 12+ 1×5 12+2× 1 12=7 12,

So the answer is: 7 12.