Diane is on a game show and she has made it to the very final round where she will have an opportunity to win a prize. For the final round, there are three doors and behind each door are eight suitcases. Each suitcase either contains a money prize or is empty. Behind the first door 7 of the suitcases are empty, behind the second door 6 of the suitcases are empty and behind the third and final door 2 of the suitcases are empty. Diane must choose a door, and once she has chosen a door she can open two of the eight suitcases and keep any prize money that she finds. Rather than just choosing among the three doors completely randomly, based on how previous contestants have performed in this final round, Diane decides to choose from the first, second and third doors with probabilities 0.51, 0.15 and 0.34, respectively. Once she has chosen a door, Diana decides to randomly open two of the eight suitcases.Find the probability that Diane goes home empty-handed.Answer:Question 1

Solve the following question and mark the most appropriate option. Opening Christmas presents was always an exciting occasion at Rachel’s house. This year, to add more fun to the occasion, she decided to pack her husband Michael’s gift in a different fashion. To wrap up the gift she first took a large box. Inside this large box, she placed 15 medium boxes of the same size. Each of these medium boxes, she either left empty or filled with 15 small boxes of the same size. In one of these small boxes, she placed the gift for Michael. When Michael unwrapped his gift, he found that 7 boxes had boxes inside them. What was the total number of empty boxes?

You have 100 doors in a row, all initially closed. You make 100 passes by the doors starting with the first door every time. The first time through, you visit every door and toggle the door (if the door is closed, you open it; if it is open, you close it). The second time you only visit every 2nd door (door #2, #4, #6, ...). The third time, every 3rd door (door #3, #6, #9, ...), and so on, until you only visit the 100th door.What state are the doors in after the last pass? Which doors are open, and which are closed?

Rachel won a money prize.She spent 36% of it on a bag and the same amount of money on a meal for her family.She saved the remaining $112.What was the total amount of her money prize?

Amy and Brad take turns rolling a fair six-sided die; first to get a "6" win. What are Amy's odds of winning if she goes first?

The organisers of an essay competition decide that a winner in thecompetition gets a prize of ` 100 and a participant who does not win getsa prize of ` 25. The total prize money distributed is ` 3,000. Find thenumber of winners, if the total number of participants is 63.