**Given: **Let A and B be two fire extinguishing engines .

The probability of availability of each of the two fire extinguishing engines is given i.e.,

P(A) = 0.95 and P(B) = 0.95

\(\Rightarrow\) P(\(\overline A\)) = 0.05 and P(\(\overline B\)) = 0.05

**To Find: **

**(i) **The probability that neither of them is available when needed

Here, P(not A and not B) = P(\(\overline A\cap \overline B\))

= P(\(\overline A\)) x P(\(\overline B\))

= 0.05 x 0.05

= 0.0025 = \(\frac{1}{100}\)

**Therefore, **The probability that neither of them is available when needed is\(\frac{1}{400}\)

**(ii)** an engine is available when needed

Here, P(A and not B or B and not A) = P( A ∩ \(\overline B\)) + P(B ∩ \(\overline A\))

= \(\frac{19}{200}\)

Therefore, The probability that an engine is available when needed is\(\frac{19}{200}\)