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A random experiment consists of tossing a coin, followed by more coin tosses depending on the results of the first toss. The coin is fair, but it is deemed to possibly come up "Heads," Tails," or "edge" poon though the last possiblity has a 0 frequency of occurrence.

The probabilities of the three possibilities (as singletons) for the first coin toss are $\frac{1}{2}, \frac{1}{2}$ and $0$ . When the first coin toss is Heads, the coin is tossed again thrice; if the first coin toss is Tails, the coin is tossed again twice; if the first coin toss is "edge," the coin is tossed again once. Each toss is made independently of any other.

Find

  1. the conditional probability that there are two "Heads" from coin tosses given that the first toss was "Heads," and
  2. the conditional probability that there is one "Heads" from coin tosses given that the first toss was "edge."

Hint: The second question (ii) answer is not $\frac{1}{2}$

I know how to do first but for second question answer is $0$ because probability of getting edge is $0$. Is it correct?

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  • $\begingroup$ The conditional probability is undefined because the event on which you are conditioning has probability zero. $\endgroup$ – angryavian Jan 22 at 6:51
  • $\begingroup$ @angryavian what is answer for first one? $\endgroup$ – maths student Jan 22 at 7:26
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yes you are correct. P(EDGE)=0, so you cannot condition on that. This is just a trick question

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  • $\begingroup$ For first one answer is 3/16 right? $\endgroup$ – maths student Jan 22 at 7:17
  • $\begingroup$ Is the conditional probability undefined, though? Sure, you can't use the standard formula, but if the coin tosses are independent, you shouldn't need to. $\endgroup$ – Arthur Jan 22 at 11:24
  • $\begingroup$ for the first question, you have already gotten one head. Since the events are independent, the way I interpret the question is that it is asking what is the probability of getting a head on flip 2 or 3 $\endgroup$ – Demetrios Papakostas Jan 22 at 18:03

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