TS EAMCET · Maths · Probability
Suppose \(E\) and \(F\) are two events of a random experiment. If the probability of occurrence of \(E\) is \(1 / 5\) and the probability of occurrence of \(F\) given \(E\) is \(1 / 10\), then the probability of non-occurrence of atleast one of the events \(E\) and \(F\) is
- A \(\frac{1}{18}\)
- B \(\frac{1}{2}\)
- C \(\frac{49}{50}\)
- D \(\frac{1}{50}\)
Answer & Solution
Correct Answer
(C) \(\frac{49}{50}\)
Step-by-step Solution
Detailed explanation
Given that, \[ P(E)=\frac{1}{5}, P(F)=\frac{1}{10} \] Probability of both occurrence, \[ P(E \cap F)=P(E) P(F) \] \[ =\frac{1}{5} \cdot \frac{1}{10}=\frac{1}{50} \] Required Probability \(=1-P(E \cap F)\) \[ =1-\frac{1}{50}=\frac{49}{50} \]
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