Consider a game in which a fair coin is tossed four times. Onetypical outcome co

Question

Consider a game in which a fair coin is tossed four times. Onetypical outcome could be represented by HT HT, which could denotethat heads occured on the first and third tosses and tails on thesecond and fourth tosses. 1) How many equally likely outcomes are there in thisgame? 2) Make a list of all the equally likely outcomes for thisgame. 3) Let A denote the event that the coin comes up heads on thethird toss. How many individual outcomes are in thisevent? 4) Let B denote the event that the coin comes up tails in thefourth too. Make a list of all the individual outcomes in B. 5) Let C denote the event that the second time that the coincomes up H is on the fourth toss. Make a list of the individualoutcomes in C.

Explanation / Answer

1.    There are 16 equally likely outcomes 2. HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT, THTH, TTHH, HTTH,HTTT, THTT, TTHT, TTTH, TTTT 3. There are 8 outcomes for which the third toss is a tail 4. (Clarification: Meaning of this statement is that tails mustoccur on the third and the fourth too) B = {HHTT, HTTT, TTTT, THTT) 5. C = {THTH, TTHH, HTTH) 6. CC= {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT,HTTT, THTT, TTHT, TTTH, TTTT}

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