Answer
$P(10~outs~in~10~consecutive~at-bats)=0.0282475249$
Work Step by Step
$P(makes~an~out)=0.70$
The events "out in at-bat 1", "out in at-bat 2", "out in at-bat 3", ..., "out in at-bat 10" are independent.
$P(10~outs~in~10~consecutive~at-bats)=P(out~in~at-bat~1)\times P(out~in~at-bat~2)\times P(out~in~at-bat~3)\times...\times P(out~in~at-bat~10)=P(makes~an~out)^{10}=0.70^{10}=0.0282475249$
