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Question

(A) Let $H$ denote the event of getting a head and $T$ denote the event of getting a tail. The experiment stops when a head appears or after three tos

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(A) Let $H$ denote the event of getting a head and $T$ denote the event of getting a tail. The experiment stops when a head appears or after three tosses.The sample space of the experiment is $S = \{H, TH, TTH, TTT\}$.Let $A$ be the event that a head does not appear on the first toss. This means the first toss is a tail $(T)$.The outcomes corresponding to event $A$ are $\{TH, TTH, TTT\}$.The probability $P(A) = P(T) = \frac{1}{2}$.Let $B$ be the event that the coin is tossed thrice. The outcomes corresponding to event $B$ are $\{TTH, TTT\}$.The intersection $A \cap B$ represents the event that the first toss is a tail $AND$ the coin is tossed thrice. This corresponds to the outcomes $\{TTH, TTT\}$.$P(A \cap B) = P(TTH) + P(TTT) = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$.We need to find the conditional probability $P(B|A)$:$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2}$.

$A$ coin is tossed until a head appears or it has been tossed thrice. Given that a head does not appear on the first toss,what is the probability that the coin is tossed thrice?

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