Question

An aircraft has three engines $A,B\&C$. The aircraft crashes if all three engines fail.

The probabilities of failure are $0.03,0.02\&0.05$ for engines $A,B\&C$ respectively.

What is the probability that the aircraft will not crash?

• A. $0.00003$
• B. $0.90$
• C. $0.99997$
• D. $0.90307$

Answer 1

The correct option is C

$0.99997$

Finding the required probability:

Given, An aircraft has three engines $A,B\&C$ & crashes when all of it's fails

Let $P\left(A\right),\hspace{0.17em}P\left(B\right)\&P\left(C\right)$ denotes the probabilities of failure of $A,B\&C$respectively. Then,

$$\begin{gathered} P\left(A\right)=0.03 \\ P\left(B\right)=0.02 \\ P\left(C\right)=0.05 \end{gathered}$$

The aircraft will crash only when all the three engine fail.

P(aircraft will crash) $=P\left(A\right)\times P\left(B\right)\times P\left(C\right)$

$$\begin{gathered} =0.03\times 0.02\times 0.05 \\ =0.00003 \end{gathered}$$

Probability of not crashing of aircraft $=1-$P(aircraft will crash)

Therefore, $$\begin{gathered} =1-0.00003 \\ =0.99997 \end{gathered}$$

Probability of not crashing of aircraft $=0.99997$

Hence, correct option is $\mathbf{\left(}\mathbf{C}\mathbf{\right)}$.