$3.(8$ points$)$ Chet is selling his best hat on eBay using a first$-$price auction. The hat has a single common true value to all the potential buyers, but the true value is unknown to everyone except himself. Potential buyers only know that the true value v is uniformly distributed between $0$ and $100.$ In other words, the probability for v to be less than or equal to an arbitrary number between $0$ and $100,$ denoted as a$,$ is P$($v $$ a$)=100*$ Tanya is very fond of hats. So the value of the hat for her is the true value plus $10.$

Chet will only accept offers that are greater than or equal to the true value.

$($a$)$ If Tanya offers $70,$ what is the probability for her offer to be accepted?