A coin is tossed until a head appears or unti | vedclass

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Question

(C) The experiment stops when a head appears or after $5$ tosses. Given that a head does not occur on the first two tosses,we have already observed $T

Vedclass · Accepted Answer

$1/4$

Vedclass · Answer

(C) The experiment stops when a head appears or after $5$ tosses. Given that a head does not occur on the first two tosses,we have already observed $TT$ (Tail,Tail). For the coin to be tossed $5$ times,we must not get a head on the $3^{rd}$ toss $AND$ we must not get a head on the $4^{th}$ toss. If we get a head on the $3^{rd}$ or $4^{th}$ toss,the experiment would stop earlier. Therefore,the sequence of outcomes for the $3^{rd}$ and $4^{th}$ tosses must be $T$ and $T$. The probability of getting a tail on any single toss is $1/2$. Thus,the probability that the coin is tossed $5$ times given the first two were tails is $P(T_3) \cdot P(T_4) = (1/2) \cdot (1/2) = 1/4$.

$A$ coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses,then the probability that the coin will be tossed $5$ times is

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