Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that: Both Anil an Ashima will not qualify the exam.

Explanation

Let E and F denote the events that Anil and Ashima will qualify the examination,
respectively.

Given that `P(E) = 0.05, P(F) = 0.10` and `P(E nn F) = 0.02`.

(a) The event "both Anil and Ashima will not qualify the examination" may be
expressed as `E' ∩ F'`.

Since, `E'` is ‘not E’, i.e., Anil will not qualify the examination and `F'` is ‘not F’, i.e., Ashima will not qualify the examination.

Also `E' ∩ F' = (E uu F)'` (by De-morgan's Law)

Now `P(E uu F) = P(E) + P(F) – P(E ∩ F)`

...