An aircraft has three engines $$A,\,B$$ and $$C$$. The aircraft crashes if all the three engines fail. The probabilities of failure are $$0.03,\,0.02$$ and $$0.05$$ for engines $$A,\,B$$ and $$C$$ respectively. What is the probability that the aircraft will not crash ?
A.
$$0.00003$$
B.
$$0.90$$
C.
$$0.99997$$
D.
$$0.90307$$
Answer :
$$0.99997$$
Solution :
Since, probabilities of failure for engines $$A,\,B$$ and $$C\,P\left( A \right),P\left( B \right)$$ and $$P\left( C \right)$$ are $$0.03,\,0.02$$ and $$0.05$$ respectively.
The aircraft will crash only when all the three engine fail.
So, probability that it crashes
$$\eqalign{
& = P\left( A \right) \times P\left( B \right) \times P\left( C \right) \cr
& = 0.03 \times 0.02 \times 0.05 \cr
& = 0.00003 \cr} $$
Hence, the probability that the aircraft will not crash $$ = 1 - 0.00003 = 0.99997$$
Releted MCQ Question on Statistics and Probability >> Probability
Releted Question 1
Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:
Two events $$A$$ and $$B$$ have probabilities 0.25 and 0.50 respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is 0.14. Then the probability that neither $$A$$ nor $$B$$ occurs is
The probability that an event $$A$$ happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is
If $$A$$ and $$B$$ are two events such that $$P(A) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left( {\frac{{\overline A }}{{\overline B }}} \right)$$ is equal to
(Here $$\overline A$$ and $$\overline B$$ are complements of $$A$$ and $$B$$ respectively).
A.
$$1 - P\left( {\frac{A}{B}} \right)$$
B.
$$1 - P\left( {\frac{{\overline A }}{B}} \right)$$
C.
$$\frac{{1 - P\left( {A \cup B} \right)}}{{P\left( {\overline B } \right)}}$$
D.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$