Ckboard. the following table displays data on whether or not a student ate breakfast the day of their exam and when and whether or not the student passed their exam for a random sample of 112 students. 1 Explain Passed Failed Total Ate Breakfast 54 12 66 8. 13) Find P Did Not Eat Breakfast 34 12 46 Total 88 24 112 1. [3] What is the probability that a randomly selected student passes their exam? 2. [3] What is the probability that a randomly selected student eats breakfast the day of their exam? the 3. [3] What is the probability that a randomly selected student passes their exam and eats breakfast the day of their exam? devi 4. [4] What is the probability that a randomly selected student passes their exam giver that they eat breakfast the day of their exam? 5. [4] What is the probability that a randomly selected student ate breakfast the day of their exam given that they passed their exam? 6. [2, 2] Are the events "passes the exam" and "eats breakfast the day of the exam" independent or dependent? Briefly explain your reasoning.Let X be the random variable representing the number of times "7" is rolled from 3 rolls of a pair of fair die. The probability distribution for this random variable is given below. roject 2 X= # of 7s Rolled P(X=x) me 0 0.57870 1 0.34722 scription 2 3 0.00463 7. [2] Explain why this is a discrete random variable. 8. [3] Find P(X=2), the missing probability from the table. 9. [3] What is the probability that 1 or fewer 7s are rolled from 3 rolls of a pair of fair dice? arce: Microsoft Excel. 10. [4] Find the mean number of 7s rolled from 3 rolls of a pair of fair dice. 11. [4] Find the variance of the number of 7s rolled from 3 rolls of a pair of fair dice. 12. [3] Find the standard deviation of the number of 7s rolled from 3 rolls of a pair of fair dice. dollars) Construction? (0 = no, 1 - yes) ral air? (0 = no, 1 = yes) Type? (2 egos, 3 a electric, 4- oil) Tine? (2 x hot air, 3= hot water, 4 to electric) Type? (s e none, 2 = private, 3 a public) Bros (lo squere fect)