A computer system uses passwords that contain exactly eight characters, and each character is one of 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9) or 38 symbols. Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Suppose that all passwords in Ω are equally likely. Determine the probability of a password containing at least 1 symbol, 1 letter, and 3 integers.

A) A computer system uses passwords that contain exactly 7 characters, and each character is 1 of the 3 lowercase letters (a, b, c) or 3 upper case letters (A, B, C) or the 5 odd digits (1, 3, 5, 7, 9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the probability that a password contains all lowercase letters given that it contains only letters. Report the answer to 3 decimal places.   B) A computer system uses passwords that contain exactly 5 characters, and each character is 1 of the 3 lowercase letters (a, b, c) or 3 upper case letters (A, B, C) or the 5 odd digits (1, 3, 5, 7, 9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the probability that a password contains at least 1 uppercase letter given that it contains only letters. Report…

Six digits are chosen randomly from the set   {0, 1,2,.....9). a.) What is the probability that all six digits are the same? b.) What is the probability that only 2 digits are the same?

There are twelve different chips in a bag: 6 red, 2 yellow and 4 blue. If two chips are drawn with replacement from the bag (one after the other), what is the probability that at least one of them is yellow? (Start with the appropriate formula in context.)

A jury pool has 24 men and 18 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, use combinations to find the probability that the jury consists of(a) all men(b) all women(c) 8 men and 4 women(d) 6 men and 6 women

Suppose that 8 people check their coats in a checkroom. If all claim checks are lost and the 8 coats are randomly returned, what is the probability that all the people will get their own coats back? The probability that all the people will get their coats back is ___

The access code for a safe consists of three digits. Each digit can be any number from 1 through 7​, and each digit can be repeated. Complete parts​ (a) through​ (c).   ​(a) Find the number of possible access codes. ​(b) What is the probability of randomly selecting the correct access code on the first​ try? ​(c) What is the probability of not selecting the correct access code on the first​ try? ​(a) Find the number of possible access codes.   The number of different codes available is nothing. ​(b) What is the probability of randomly selecting the correct access code on the first​ try?   The probability of randomly selecting the correct access code is nothing. ​(Round to three decimal places as​ needed.) ​(c) What is the probability of not selecting the correct access code on the first​ try?   The probability of not selecting the correct access code is nothing. ​(Round to three decimal places as​ needed.)

A planned community has 150 homes, each with an automatic garage door opener. The door opener has seven switches that a homeowner can set to 0 or 1. For example, a door opener code might be 1001100. Assuming all the homes in the community are sold, what is the probability that at least two homeowners will set their switches to the same code, and will therefore be able to open each other's garage doors?