A drunken man who has n keys wants to open the door if his office. He tries the keys at random, one by one, and the unsuccessful keys are eliminated. Show that at all times, no matter how many unsuccessful keys he has eliminated, the probability of finally locating the correct key is 1/n

Abigail needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine, to the nearest percent, the probability that her password will be greater than 6300.

In a large school, it was found that 71% of students are taking a math class, 72% of student are taking an English class, and 93% of students are taking both. Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary. Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.

Thomas stands on a street corner tossing a coin. He decides he will toss the coin 10​ times, each time walking 1 block north if it lands heads​ up, and 1 block south if it lands tails up. Find the probability that he ends up 6 blocks south of his original corner.