While a regular coin is unlikely to land on its side, one can glue together seve
ID: 3048207 • Letter: W
Question
While a regular coin is unlikely to land on its side, one can glue together several coins and thus create a ``three-sided coin’’ that has equal probability of landing ``Heads’’, ``Tails’’, and ``Side’’. 1) Suppose we toss such a three-sided coin twice. (a)What is the best sample space S? (b)Are outcomes in this space equally likely? (c)What is the probability that the three-sided coin lands on its ``Side’’ at least once? Suppose we toss the three-sided coin three times. (d)Is getting Heads-Heads-Heads more likely than getting Heads-Tail-Side?
Explanation / Answer
a) let ``Heads’’, ``Tails’’, and ``Side’’ are denoted by H; T and S
therefore sample space S ={ HH ; HT ; HS ; TH ;SH ;TT ;TS ;ST ;SS} ( 9 outcome
b) yes all outcome are equally likely as events are indepdnent and probability of a outcome =1/9
c) probability that the three-sided coin lands on its ``Side’’ at least =5/9
d)
no as events are independent therefore probability of Heads-Heads-Heads is same as probability of Heads-Tail-Side.
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