{enumerate} m Find the conditional probability that both coins show a head given the first shows a head. m Find the conditional probability that both coins show a head given at least one of them is a head. {enumerate}

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Chapter1: Combinatorial Analysis
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Suppose we model tossing a coin with two outcomes, H and T, representing heads and tails. Let
Pr(H) = Pr(T)
{H, T}² represents two coin tosses and that the tosses are
independent.
=
Suppose Ω
=
\begin{enumerate}
\item Find the conditional probability that both coins show a head given the first shows a head.
\item Find the conditional probability that both coins show a head given at least one of them is a head.
\end{enumerate}
Transcribed Image Text:Suppose we model tossing a coin with two outcomes, H and T, representing heads and tails. Let Pr(H) = Pr(T) {H, T}² represents two coin tosses and that the tosses are independent. = Suppose Ω = \begin{enumerate} \item Find the conditional probability that both coins show a head given the first shows a head. \item Find the conditional probability that both coins show a head given at least one of them is a head. \end{enumerate}
Expert Solution
Step 1

In tossing a coin two times, the possible outcomes are

{(H, H), (H,T), (T, H), (T, T)}

Let us define some events

A : both coin shows head.

B : first coin shows head.

C : at least a coin shows head.

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