Answer
$P(5~consecutive~outs~and~reaches~base~safely)=0.050421$
Work Step by Step
$P(reaches~base~safely)=0.30$ and $P(makes~an~out)=0.70$
The events "out in at-bat 1", "out in at-bat 2", "out in at-bat 3", "out in at-bat 4", "out in at-bat 5" and "reaches base safely" are independent.
Now, using the Multiplication Rule (see page 282):
$P(5~consecutive~outs~and~reaches~base~safely)=P(out~in~at~bat~1)\times P(out~in~at~bat~2)\times P(out~in~at~bat~3)\times P(out~in~at~bat~4)\times P(out~in~at~bat~5)\times P(reaches~base~safely)=0.70\times0.70\times0.70\times0.70\times0.70\times0.30=0.050421$
