SOLVED:a. \quad A balanced coin is tossed twice. List a sample space showing the possible outcomes. b. \quad A biased coin (it favors heads in a ratio of 3 to 1 ) is tossed twice. List a sample space

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for question 4.24 apart. A. Ask this to list the sample space if a poise coin is tossed twice, so the sample distribution space is just all of the possible outcomes. So we have get tales and tails. We can get tails and heads. We could get heads and tails, or we could get heads and heads. nowadays this forms a proper sample space because each chemical element in the sample outer space is equally probably to occur. then, for Part B, we ‘re told that the coin is biased and it favors heads in a ratio of 3 to 1. And once again, the coins tossed doubly and were spliced Willis the sample space of all possible outcomes. So this is a bite catchy, since if we just tilt of these outcomes, it would not make a proper sample space, because nowadays that we have a biased coin, the unlike outcomes are not equally likely. Heads are more likely than tails, so some of these outcomes in particular heads and heads, are more likely than some of the other outcomes, such as tales and tails. so to account for the fact that heads are more coarse than tails, we can take the outcomes that are more likely and represent them in the sample distribution distance more frequently. So we can say that the sample outer space has elements that are equally likely but the different probabilities of different outcomes there, represented by the fact that they show up in the sample space more often. then, for exemplar, if we take yeah, consequence pales and tails and the result heads and tails now, since Heads is 3 to 1, has an odds proportion of 3 to 1 compared to tales. We should represent this result three times compared to the one time that the tales and tales is represented. similarly, the result hails. Heads should be represented three times using the like logic now for heads and heads, it gets a bit catchy. sol for the first, a coin flip, the odds ratio is 3 to 1 in favor of heads over tails. But for the moment coin toss, the odds ratio is 3 to 1 in privilege of heads over tails besides, so that ‘s an overall odds ratio of 9 to 1 for heads and heads compared to tales and tails. so this result must be represented nine times. so now we ‘re ready to enter the sample outer space. So narrative and tails and I ‘m decidedly gon na run out of distance here, so I ‘ll just clear a little sting of of this out of the way for us. So we ‘ve got the one tales and tails the three tails and heads the three heads and tails. And now we need the nine heads and heads, and I believe that ‘s nine heads and heads. So this is a sample space for region B.

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