According to an article, $75\%$ of high school seniors have a driver's license. Suppose we take a random sample of $100$ high school seniors and find the proportion who have a driver's license. Find the probability that more than $77\%$ of the sample have a driver's license. Begin by verifying that the conditions for the Central Limit Theorem for Sample Proportions have been met.

First, verify that the conditions of the Central Limit Theorem are met.

The Random and Independent condition holds assuming independence.

The Large Samples condition holds.

The Big Populations condition reasonably be assumed to hold.

The probability that more than $77\%$ of the sample have a driver's license is

$($Type an integer or decimal rounded to three decimal places as needed.$)$