Question

Hi, can you help me with this question, please, thank you:)

Answer 1

The defect rate of the machine is 8%.

The number of items that are chosen is 6.

To find the probability that at least one will have a defect can be calculated by the formula:

`P(x)=(n!)/(x!(n-x)!)p^xq^(n-x)`

Where n is the number of trials (6)

x is the number of successes desired (1)

p is the probability of getting a success in one trial (8%=0.08)

q=1-p is the probability of getting a failure in one trial (1-0.08=0.92)

By replacing these values you will find the probability:

`\begin{gathered} P(1)=(6!)/(1!(6-1)!)0.08^10.92^(6-1) \\ P(1)=6*0.08*0.6591 \\ P(1)=0.3164 \end{gathered}`

Then, the probability that at least one item will have a defect is 0.3164.