Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 5; B: the numbers add to 6; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbolic form. Either the numbers add to 6, or they add to 10, or at least one of them is 1. O B'u D'u C Bu D'u C' BuD'uC BuD'n C Bn D'uC How many elements does it contain?

Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.

A. Suppose you close your eyes and randomly select one M&M from your pile, find the probability of grabbing a color that contains the letter “r”or a color that contains the letter “o”. B. Suppose you close your eyes and randomly select one M&M from your pile, replace that M&M, and select another M&M from the pile. What is the probability that you will select an orange and a yellow M&M? C. Suppose you close your eyes and randomly select two M&M’s from your pile, without replacing the first M&M. What is the probability that you will select a red and a blue M&M?

2 dice, one green and one black, are rolled once. Which of the following events are independent?A. E = A 2 is rolled on the green die, F = A sum of 8 is rolled on both dice.B. E = A sum of 3 is rolled on both dice, F = A 4 is rolled on the black die.C. E = A 2 is rolled on the green die, F = A sum of 7 is rolled on both dice.D. E = A 3 is rolled on the green die, F = A 5 is rolled on the black die.

PLEASE SELECT WHICH OF THE FOLLOWING IS/ARE TRUE AND EXPLAIN. Please answer within 30 minutes.

See pictures for questions a and b. Write your answers as fractions. Problem A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions.