MHT CET · Maths · Probability
The odds against a certain event are \(5: 2\) and the odds in favour of another independent event are \(6: 5 .\) The probability that at least one of the events will happen, is
- A \(\frac{25}{77}\)
- B \(\frac{52}{77}\)
- C \(\frac{12}{77}\)
- D \(\frac{65}{77}\)
Answer & Solution
Correct Answer
(B) \(\frac{52}{77}\)
Step-by-step Solution
Detailed explanation
Let \(A\) and \(B\) are two given events.
\(
\begin{array}{l}
\therefore P(A)=\frac{2}{7}, P(B)=\frac{6}{11} \\
\therefore \text {Required probability }=1-P(\bar{A}) P(\bar{B}) \\
=1-\left(1-\frac{2}{7}\right)\left(1-\frac{6}{11}\right) \\
=\frac{52}{77}
\end{array}
\)
\(
\begin{array}{l}
\therefore P(A)=\frac{2}{7}, P(B)=\frac{6}{11} \\
\therefore \text {Required probability }=1-P(\bar{A}) P(\bar{B}) \\
=1-\left(1-\frac{2}{7}\right)\left(1-\frac{6}{11}\right) \\
=\frac{52}{77}
\end{array}
\)
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