Question 5. Suppose there are six students. Assume each student chooses to sit down at table 1 with a probability of 0.6 and at table 2 with a probability of 0.4. Each student makes their decision independently. Let N denote the number of chairs at each table. (a) Let N-4. What is the probability that table 1 is full, i.e, at least four students choose to sit down at table 1? (b) Find the smallest possible integer N such that the probability of table 1 being full is less than 10%.

Q4. There are two urns. The first urn contains 3 white and 7 black balls; the second contains 6 white and 4 black balls. One ball is taken out of the first urn at random and and put it into the second urn, and then one ball was taken out of the second urn. (a) Find the probability that the removed ball is white. (b) It is known that the ball taken from the second urn was white. Find the probability that a white ball was transferred from the first urn to the second.

A group consists of 5 Democrats and 8 Republicans. 7 people are selected to attend a conference.a. In how many ways can 7 people be selected from this group of 13​?b. In how many ways can 7 Republicans be selected from the 8 ​Republicans?c. Find the probability that the selected group will consist of all Republicans.

The mall has a set of data with employee age (X) and the corresponding number of annual on-the-job-accidents(Y). Analysis on the set finds that the regression equation is Y=100-3X. What is the likely number of accidents for someone aged 30?     97     100     10     none of the above

A bag contains 11 Blue balls, 9 Red balls, and 10 Green balls. Two balls are going to be drawn from the bag (one at a time) and then returned to the bag before the next is drawn. Let event B = blue ball chosen, R = Red ball chosen, and G- Green ball chosen. What is the probability the first is blue and the second is red? What is P(B and then R)? Write an answer to 4 decimal places.

fair die is rolled three times. A 5 is considered "success," while all other outcomes are "failures." Find the probability of 2 successes. The probability of 2 successes is (Type an integer or a simplified fraction.) ...

There are two boxes. Box A contains 6 red balls, and 4 blue balls andBox B contains 4 red balls and 8 blue balls. A die is rolled, if the number is lessthan 3, a ball is selected from box A. If the result is 3 or more, a ball is selectedfrom Box B. Calculate:a. The probability that the ball will be red and selected from Box B.b. The probability that the ball will be blue.

Three cards are selected one by one from a shuffled deck of playing cards. Each is replaced after being recorded before the next card is drawn.What is the probability that among the 3 cards recorded there is at least one diamond card?Enter your answer as a fraction in lowest terms.

The mean weight of a Great Dane is 63.0 kg with a standard deviation of 2.3 kg.  Suppose a researcher randomly samples 61 Great Danes and records the weights of the sampled dogs.  Calculate the standard deviation of the mean, rounded to 2 decimal places

Keno is a casino game in which the player has a card with the numbers 1 through 80 on it. The player selects a set of k numbers from the card, where k can range from one to ifteen. The “caller” announces twenty winning numbers, chosen at random from the eighty. The amount won depends on how many of the called numbers match those the player chose. Suppose the player picks ten numbers. What is the probability that among those ten are six winning numbers?