(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 3-bit character consists of 0's and 1's. The values of the bits are determined by tosses of a fair coin.

(a) Find the probability that the first bit is 1.

(b) Find the probability that the first bit AND the third bit are 1.

(b) Find the probability that the first bit is 1 if the coin is biased.

3. The attempt at a solution

(a) There are 8 possible combinations of bits. Of these 8, 4 of them have 1s as the first digit so I get P(A) = 4/8. I am confused though.. is this the right logic? I thought about it another way where P(A) = 1/2 because the coin can land on heads or tails, so there is an equal chance that it would be either 0 or 1. I know both methods of thinking give the same answer, but I'm not sure which is most correct.

(b) Again, since I'm unsure about the method I'm not sure what the correct way to go about this is. I get P(B) = 2/8 from looking at this set {000, 001, 010, 011, 100, 101, 110, 111}. I get P(B) = (1/2)*(1/2) = 1/4 if I do it based on coin flip (I don't think it's mutually exclusive because they could both be 0 or both be 1, but I might be incorrect). Again both are equal.

(c) I don't know where to start on this one because the question doesn't state any values for the bias. Is there a general rule for this?

Any help would be appreciated! Thanks.

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# Homework Help: Fair vs. biased coin probability

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