A. A m coin is tossed four times. Use H to denote heads and T to denote tails (e.g. HTHH represents the sequence heads, tails, heads, heads during the tosses). i. ii. iii. iv. v. vi. List the elements of the sample space (using a tree diagram can help) List the elements that belong in each of the following event. Event A: the coin turned up heads 0 times. Event B: the coin tumed up heads 1 time. Event C: the rst two tosses came up heads. Event D: the coin turned up heads more than 1 time. Are the following pair of events mutually exclusive (answer YES or NO and provide a brief explanation)? - A and B o B and C 0 C and D Compute the probability P(A U B). Compute the probability P(C U D). Compute the probability P(C n D). B. For the sample space S = {0,1 ,2,3,4,5,6,7,8}, it is known that an odd numbered outcome is twice as likely as an even numbered outcome, with P(O) = P(2) = P(4) = P(6) = P(B) and P(l) = P(3) = P(S) = P(7). Events are dened as follows (Is zero even?: hpsszxoutube/StlTC-SOLdM ): ii. X = even number Y = greater than or equal to 6 Z = {2,4} Similar to the diagram sketched in class for the die roll, sketch a Venn diagram showing the sample space and eventsX, Y, and Z. All 9 elements of S must appear on the diagram in their proper events. For each of the following, give the resulting set of elements AND compute the probability: I Z U 1' X U Y X' n 2 (X n Z)' (X U Y) n Z (X n Z) U 1