Question

Find the indicated probability. Round to three decimal places.A machine has 6 identical components which function independently. The probability that a component will fail is 0.3. Themachine will stop working if more than two components fail. Find the probability that the machine will be working.

Answer 1

Answer: 74.43%

Let us first list down the probabilities of the machine working.

First is the probability that none of the components will fail. We can write this probability as:

`P(0)=(1-0.3)^6`

Next, the probability that one of the components will fail. This will give us:

`P(1)=C^1_6(1-0.3)^5(0.3)`

Then, the probability that 2 of the components will fail.

`P(2)=C^2_6(1-0.3)^4(0.3)^2`

Adding all of these probabilities and we will have:

`P=(1-0.3)^6+C^1_6(1-0.3)^5(0.3)+C^2_6(1-0.3)^4(0.3)^2`
`P=(0.7)^6+(6)(0.7)^5(0.3)+(15)(0.7)^4(0.3)^2`
`P=0.74431*100=74.43\%`

Therefore, the probability that the machine will be working would be 74.43%.