A binary communication channel transmits a sequence of "bits" (0s and 1s). Suppose that for any particular bit transmitted, there is a 15% chance of a transmission error (a 0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently of one another. (Round your answers to four decimal places.) (a) Consider transmitting 1000 bits. What is the approximate probability that at most 175 transmission errors occur?   (b)

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.

in a lottery game a single ball is drawn at random from a container that contains 25 identical balls numbered 1 through 25. Find the probability that the number drawn is a miltiple of 11 or a multiple of 4.

Each of the numbers 0 - 9 is written on a sheet of paper and the ten sheets of paper are placed in a box If two of these sheets of paper are selected from the box at random, without replacement, find the probability that both numbers are greater than 7.

Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.

section 5.3 Out of 413 applicants for a job, 127 have over 10 years of experience and 51 have over 10 years of experience and have a graduate degree.   Step 1 of 2 :   What is the probability that a randomly chosen applicant has a graduate degree, given that they have over 10 years of experience? Enter a fraction or round your answer to 4 decimal places, if necessary.   Step 2 of 2: Consider that 83 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 10 yrs of experience, given that the applicant has a graduate degree? round to 4 decimal places