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A
coin is tossed twice. (a) Indicate a sample space for this experiment. (b) Indicate also a sample space for the number of heads obtained. Solutions (a) A coin has two sides, heads and tails. If the coin is tossed once, then either H (heads) or T (tails) could occur. If it is tossed twice, both heads could occur. Both tails could occur also. Likewise, either heads or tails could occur on either toss. The appropriate sample space S for this experiment would be the set of possible outcomes, being S = {TT, HH, TH, HT}. Both letters together represent the possibilities of the first and second toss. (b) For the number of heads, there could be 1 (one) on the first toss and 1 on the second, making it 2 heads. There could also be 1 on the first and 0 (none) on the second. Vice versa, there could be 0 on the first and 1 on the second. There could even be 0 on both tosses. The sample space then for this would be S = {2, 1, 0}. |
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