b), A quarter was tossed four times and we have sixteen (16) possible outcomes i
ID: 3051236 • Letter: B
Question
b), A quarter was tossed four times and we have sixteen (16) possible outcomes in the sample space. ),List these sixteen possible outcomes in the sample space. (8 points) (i).What is the probability that the last toss is heads? (3 points) Gii). What is the probability that the last toss is tails? (3 points) Gv). What is the probability that we have at least two tails? (3 points) v)What is the probability of having at most two tails? (3 points) vü. What is the probability of having exactly four heads? (3 points) vi). What is the probability of having exactly four tails? (3 points). [Hint: HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads.],Explanation / Answer
(i) 16 possible outcomes are:
{HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, TTHH, THHT, THTH, HTTT, THTT, TTHT, TTTH, TTTT}. (Ans).
(ii) The probability that the last toss is heads = 8/16 = 0.5.
(Ans).
(iii) The probability that the last toss is tails = 8/16 = 0.5. (Ans).
(iv) The probability that we have at least 2 tails = 11/16 = 0.6875. (Ans).
(v) The probability of having at most 2 tails = 11/16 = 0.6875. (Ans).
(vi) The probability of having exactly 4 heads = 1/16 = 0.0625. (Ans).
(vii) The probability of having exactly 2 tails = 6/16 = 0.375. (Ans).
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