A message is transmitted using a binary code of Os and 1s. Each transmitted bit (0 or 1) must pass through three relays before reaching a receiver. At each relay, the probability is .20 that the bit sent is different from the bit received (a reversal). Assume that relays operate independently of one another. Transmitter -> Relay 1 -> Relay 2 -> Relay 3 -> Receiver If a 1 is sent from the transmitter, what is the probability that a 1 is sent by all three relays?

Each of the numbers 5 - 15 is written on a sheet of paper. The eleven sheets of paper are placed in a small wicker basket. If two of these eleven sheets of paper are selected from a basket, without replacement, find the probability that neither number is odd.

Assume that when an adult is randomly​ selected, the probability that they do not require vision correction is 18​%.  If 7 adults are randomly​ selected, find the probability that exactly 2 of them do not require a vision correction. if  adults are randomly selected the probability that exactly 2 of them do not require a vision correction is _________.  (ROUND TO THREE DECIMAL PLACES AS NEEDED)

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.

Suppose that the probability that a light bulb works is 0.95. If there are 4 light bulbs in a straight of light bulbs and each of these light bulbs work independently what is the probability that all of them work? 0.90 0.97 0.95 0.81

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.

A prize is placed at random in one of three boxes. You pick a box (and do not open it). Now, the dealer (who knows where the prize is) chooses one of the other two boxes, opens it and shows you that it is empty. She then gives you the opportunity to keep your original box or switch to the other unopened box. Find the probability of winning the prize if you switch. Find the probability of winning the prize if you stay. Should you stay or switch?