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A fair coin is tossed 7 times. (a) i. Use counting methods to nd the probability of getting 7 consecutive heads HHHHHHH . ii. Use counting methods to nd the probability of getting the sequence HTTHTHH iii. Common sense and experience in cointossing might suggest that obtaining a pattern of 7 con secutive heads in (i) is far less likely than obtaining the pattern we see in (ii). Is this a awed viewpoint? Give a clear decisive answer. Vague answers will not receive marks. To help you with this last question, why is it far more likely to get a pattern (with 4 heads) as in part (ii) than a string with 8 heads as in part (i)? Do a calculation to back up your answer. (b) Let X be the discrete random variable representing the number of heads which can occur. Find the discrete probability distribution of X and present in a Table similar to the following. X:a:z- 0 1 2 3 4 5 6 7 (0) Determine the Expected value p : E(X) of X. Here you are required to use the formula for Expected Values that was given in the class-notes and in class