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

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(C) Let $T$ denote a tail and $H$ denote a head. Given that a head does not occur on the first two tosses,the outcomes for the first two tosses are $(

Vedclass · Accepted Answer

$\frac{1}{4}$

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(C) Let $T$ denote a tail and $H$ denote a head. Given that a head does not occur on the first two tosses,the outcomes for the first two tosses are $(T, T)$. The experiment continues until a head appears or the coin is tossed $5$ times. For the coin to be tossed $5$ times,we must not get a head on the $3^{rd}$ and $4^{th}$ tosses. The probability of getting a tail on the $3^{rd}$ toss is $P(T_3) = \frac{1}{2}$. The probability of getting a tail on the $4^{th}$ toss is $P(T_4) = \frac{1}{2}$. Since these are independent events,the probability that the coin is tossed $5$ times given the first two were tails is $P(T_3) 	imes P(T_4) = \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{4}$.

$A$ 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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