flipped. If it shows heads, you draw a marble from shows tails, you draw a marble from urn B with 3 of choosing a blue marble, given that the coin sh
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- A die has 4 faces with A, 2 faces with B. Jar A contains 3 red and 2 green tickets, while Jar B contains 1 red and 4 green tickets. A roll is used to determine which jar is selected then tickets are drawn simultaneously. a. P(both are green tickets) b. P(one red and one green ticket from jar B) C. P(both tickets are red given they came from jar A)Use permutations to solve. The student activity club at the college has 39 members. In how many different ways can the club select a president, a vice president, a treasurer, and a secretary? Substitute values into the formula for npr. nPr= ...Green Red Orange Purple Yellow 3. Caitlyn and Tabitha want to fairly decide who will take the family dog on a walk, so they roll a fair six-sided die and spin the spinner above. Caitlyn will walk the dog if the die roll is a 1, 2, or 3 and the spinner lands on orange or green. Tabitha will walk the dog if the die roll is a 4 or 6 and the spinner lands on red, yellow, or purple. They will continue the experiment until one of the events occurs. Does the experiment provide a fair way to decide who walks the dog? Explain using probability.
- Ali and Ahmet play a game. A fair die is rolled, and each time it is thrown it is equally likely to show any of the six numbers. If it shows 5, Ali wins. If it shows 1, 2 or 6, Ahmet wins. Otherwise, they play a second round and so on. What is P(Ali wins on 5-th round)=? O a. 1/96 O b. 1/162 O c. 1/243 O d. 1/486In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Anne, Ben, Collin, and Daisy. The possible outcomes can be represented as follows. АВ, АС, AD, BC, BD, CD, ВА, СА, DA, CВ, DB, DC Here, for example, AD represents the outcome that Anne receives the first prize and Daisy receives the second prize. Let = event that Collin gets first prize Y = event that Daisy gets a prize Z= event that both price winners are boys.Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can the three movies be chosen?
- In the game of dominoes each piece is marked with two numbers. The pieces are symmetrical, so that the number pair is not ordered (for example, (2,6)=(6,2)). How many different pieces can be formed using the numbers 1, 2, . . . , n?Suppose Fred has 2 pairs of pants (blue and black) and 3 shirts (red, blue, and black). Which of the following represents all of the outfits Fred could make with these options?Provide the complete solution and illustration
- In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Anne, Ben, Collin, and Daisy. The possible outcomes can be represented as follows. АВ, АС, AD, BC, BD, CD, ВА, СА, DA, CВ, DB, DC Here, for example, AD represents the outcome that Anne receives the first prize and Daisy receives the second prize. Let = event that Collin gets first prize Y = event that Daisy gets a prize Z= event that both price winners are boys.A game consists of spinning a spinner and then rolling a number cube. The spinner is equally likely to land on any 1 of the 4 colors red, yellow, green, or blue. The number cube is equally likely to land with any of the 6 sides labeled 1 through 6 up. To win the game, a contestant must either spin red and roll any number or spin a color other than red and roll a 6. In other words, the contestant must either spin red or roll a 6 to win. Draw a rectangular model to go along with this problem.Joe owns a coin that is either a fair coin or a two-headedcoin. Imelda believes that there is a 12chance that the coinis two-headed. She must guess what kind of coin Joe has. Ifshe guesses correctly, she pays Joe nothing, but if sheguesses incorrectly, she must pay Joe $2. Before guessing,she may pay 30¢ to see the result of a single coin toss (headsor tails). Determine how Imelda should minimize herexpected loss. Also determine EVSI and EVPI.