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If $80 \%$ of flights depart on time, $70 \%$ of flights arrive on time and $65 \%$ of flights depart on time and arrive on time, then the probability that a flight that has just departed on time will arrive on time is
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Verified Answer
The correct answer is:
$\frac{13}{16}$
Consider the event
$A=$ Flight departs on time
$B=$ Flight arrive of time
$$
\begin{gathered}
p(A)=80 \%, p(B)=70 \%, p(A \cap B)=65 \% \\
\text { Required probability }=P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)} \\
=\frac{65 \%}{80 \%}=\frac{13}{16}
\end{gathered}
$$
$A=$ Flight departs on time
$B=$ Flight arrive of time
$$
\begin{gathered}
p(A)=80 \%, p(B)=70 \%, p(A \cap B)=65 \% \\
\text { Required probability }=P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)} \\
=\frac{65 \%}{80 \%}=\frac{13}{16}
\end{gathered}
$$
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