I need help with my attached statistics questions.

Professor Duque will participate in a lottery that will be played by five hundred participants. He buys a ticket for five dollars. If the lucky randomly selected winner gets one hundred dollars as a prize, what would Duque's expected winnings or losses be? (Show your calculations, interpret your results, and make sure you answer the question!) (17 points)An experiment is rolling a fair die and then flipping a coin. a} State the sample space. List outcomes separated by commas. Use notation like 1H to mean you rolled a 1 on the die and flipped heads on the coin. {I I} b] Find the probability of getting a tail. Leave your answer as a fraction. :1} Find the probability of getting a a. Leave your answer as a fraction. d] Find the probability of getting a 3 or a head. Leave your answer as a fraction. e} Find the probability of getting a 1 and a tail. Leave your answer as a fraction. An experiment is to draw '1 card from a fair deck of playing cards. a} If you were to list the sample space. how many equally likely outoomes would it haye? b] Find the probability of getting a a. Lease your answer as a fraction. I I :1} Find the probability of not getting a heart. Leave your answer as a fraction. I I d] Find the probability of getting a club. Leave your answer as a fraction. I I e} Find the probability of getting a s or a spade. Leave your answer as a fraction. I I Suppose the spinner shown below is used for a game. 12 11 2 10 3 A 5 7 6 Find the probability of each event below. Write all probabilities as fractions in simplest form. (a) P(spin 6) = (b) P(spin 7 or 12) = (c) P(spin a multiple of 4) = (d) P(spin a number more than 7) =Consider two events, A and B, with the following probabilities: P(A) = 0.42 P(B) = 0.36 P(An B) = 0.12 Find the probability of A U B . Round to the nearest hundredth as needed. Hint: You can use a Venn diagram or the Additive Rule for probability. P(A U B) =Here is the probability model for the blood type of a randomly chosen person in the United States. Brood Tree nun \"mm Maria has type B blood. She can safely receiye blood transfusions from people 1with blood types 0 and B. What is the probability that a randomly chosen American can donate blood to Maria? Give the answer as a decimal. A jar contains 10 red marbles numbered 1 to 10 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions. (a) The marble is red. P(red)= (b) The marble is odd-numbered. P(odd)= (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =Let A and B be mutually exclusive events, such that P(A) = 0.7295 and P(B) = 0.1734 . Find the following probabilities: P(A and B)= (Round the answer to 4 decimals) P(A or B)= (Round the answer to 4 decimals)On a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong? Give your answer as a fractionGiving a test to a group of students, the grades and gender are summarized below A B C Total Male 12 10 11 33 Female 9 4 7 20 Total 21 14 18 53 If one student is chosen at random, Find the probability that the student did NOT get an "C"A bag of MOM's has 5 red, 6 green, 2 blue, and 4 yellow M&M's. Suppose you randomly select two MOM's from the bag one at a time without replacing the first MOM. Let A = first MOM is yellow and B = second MOM is red. Find the following probabilities. (Write your answers as fractions.) a) P(A) b) P(B | A) = c) P(A and B) =Suppose a math class contains 31 students, 19 females (three of whom speak French) and 12 males (four of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.Find the mean of this probability distribution. Round your answer to one decimal place. H : Find the standard deviation of this probability.r distribution. Give your answer to 1 decimal places. gr: The probability distribution for the number of students in Statistics classes offered at a small college is given, but one value is missing. Fill in the missing value, then answer the questions that follow. 'r'ou may round your answers to two decimal places, if necessary. Find the mean number of students in a Statistics class at the college: Find the standard deviation of the number of students in a Statistics class at the college