Suppose you roll two fair, six-sided dice - one red and one green. The following figure shows the sample space of this chance process. Are the events "sum is 8" and "green die shows a 4" independent? Justify your answer. P(sum of 8) = 3 = 0.1398 and P(sum of 8 | green is 4) = = 0.1667 36 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent. OP(sum of 8) == 0.1667 and P(sum of 8 | green is 4) = = = 0.1667 6 Because these two probabilities are equal, the events "sum is 8" and "green die shows a 4" are independent. P(sum of 8) == 0.1398 and P(sum of 8 | green is 4) = = = 0.2 36 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent. P(sum of 8) = 36 = 0.1398 and P(sum of 8 | green is 4) == 0.1667 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are independent. P(sum of 8 and green is 4) = 3 = 0.278 and P(sum of 8 and not green is 4) = 3 = 0.111 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent.

Question 1Suppose we have an experiment that consists of flipping a coin 5 times.i. Find the total number for the outcomes for this experiment? ii. List all the elements in the sample space?iii. Find the probability that tails will be occurring at least 2 times on three coin flips?iv. Find the probability of getting all Head and all Tail on five coin flips?Question 2A bag has 10 blue balls and 5 red balls. 2 balls are to be drawn successively and without replacement. What is the probability that the first ball is red and the second is blue?Question 3Two coins are loaded so that each comes up heads 80% of the time when tossed. If the coins are both tossed simultaneously, i. What probability will the result be both are Tail?ii. What probability will the result give Head and Tail?

A couple plans to have four children. The father notes that the sample space for the number of girls the couple can have is 0, 1, 2, 3, and 4. He goes on to say that since there are five outcomes in the sample space, and since each child is eaually iikely to be a boy or girl, all five outcomes must be equally ieiy. Therefore, the probability of all four children being girls is 1/5. Explain the flaw in his reasoning. The argument is only correct if each child is equally likely to be a boy or girl. O The outcomes are not equally likely. O The sample space has less than 5 possible outcomes. O The sample space has more than 5 possible outcomes.

An experiment consists of tossing a coin three times. What is the sample space of this experiment? What subset of outcomes is the event that the experiment results in more heads than tails?