Consider a binary code with 4 bits (0 or 1) in each code word. In each code word, a bit is a zero with probability 0.6, independent of any other bit.

The access code for a garage door 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 jury pool has 23 people that are married and 21 people that are not married, 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 without replacement, find the probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.) (a) all married people. (b) all not married people. (c) 8 married and 4 that are not married. (d) 6 married and 6 that are not married.

each of the natural numbers from 1 to 15 inclusive is written on one card, and different numbers are written on the different cards. We randomly select four cards. What is the probability that the smallest number of selected cards is 8 or the largest of them is 12?