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QUESTION

# A balanced coin is tossed 8 times. (a) How many outcomes of this experiment are possible?

A balanced coin is tossed 8 times. (a) How many outcomes of this experiment are possible? Assume we observe the order order in which each flip results. (b) How many outcomes have exactly k heads, where k = 0, 1, 2, 3, 4, 5, 6, 7, 8? Clearly label each. (c) Let Ak be the event that we observe exactly k heads (k = 0,1,...,8). Compute P(Ak). (d) Let F be the event that the first three of the 8 tosses result in exactly one head. Compute P (F ). (e) Let G be the event that the last five of the 8 tosses result in exactly three heads. Compute P (G). (f) Compute P (F ∩ G) and P (F ∪ G). Clearly label each. (g) Compute P(F|A4).