the probability that an engine will not start is 0.04. a rocket has four independent engines. what is the probability that at least one of the engines does not start?

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Accepted Answer

# Explanation:
## Step1: Calculate the probability that an engine starts
The probability that an engine starts is $1 - 0.04=0.96$

## Step2: Calculate the probability that all four engines start
Since the engines are independent, the probability that all four engines start is $0.96\times0.96\times0.96\times0.96=(0.96)^{4}$
$$
\begin{align*}
(0.96)^{4}&=(1 - 0.04)^{4}\
&=1-4\times0.04 + 6\times(0.04)^{2}-4\times(0.04)^{3}+(0.04)^{4}\
&=1 - 0.16+6\times0.0016 - 4\times0.000064+0.00000256\
&=1 - 0.16 + 0.0096-0.000256 + 0.00000256\
&=0.8493
\end{align*}
$$

## Step3: Calculate the probability that at least one engine does not start
The probability that at least one engine does not start is $1-(0.96)^{4}$
$$1 - 0.8493=0.1507$$

# Answer:
$0.1507$

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Question

Explanation:

Step1: Calculate the probability that an engine starts

Step2: Calculate the probability that all four engines start

Step3: Calculate the probability that at least one engine does not start

Answer: