TS EAMCET · Maths · Probability
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
- A \(\frac{13}{16}\)
- B \(\frac{11}{16}\)
- C \(\frac{13}{14}\)
- D \(\frac{11}{14}\)
Answer & Solution
Correct Answer
(A) \(\frac{13}{16}\)
Step-by-step Solution
Detailed explanation
Consider the event \(A=\) Flight departs on time \(B=\) Flight arrive of time \[ \begin{gathered} p(A)=80 \%, p(B)=70 \%, p(A \cap B)=65 \% \\ \text { Required probability }=P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)} \\ =\frac{65 \%}{80 \%}=\frac{13}{16} \end{gathered} \]
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