Question

Question 12 Assignment from the math book A manufacturing machine has a 8% defect rate.If 3 items are chosen at random, what is the probability that at least one will have a defect? Round your answer to three decimal places.A good calculator is found at: Stattrek Binomial Calculator _______. A good video for using the TI84 is TI84 and the Binomial Probability ______.

Answer 1

It is given that,

`\begin{gathered} p\text{ = 8\% = 0.08} \\ n\text{ = 3} \end{gathered}`

By applying Binomial distribution,

`\begin{gathered} P(x\ge1)\text{ = 1 - P\lparen x}<1) \\ P(x\ge1)\text{ = 1- P \lparen x = 0 \rparen} \end{gathered}`

Substituting the value in the formula,

`\begin{gathered} P(x\ge1)\text{ = 1 - }^3C_x\left(0.08\right)^x\left(1-0.08\right)^(3-x) \\ P(x\ge1)=\text{ 1 - }^3\text{C}_x\left(0.08\right)^x\left(0.92\right)^(3-x)\text{ \_\_\_\_\_\_\_\_ x = 0, 1, 2, 3} \end{gathered}`
`\begin{gathered} P(x\ge1)\text{ = 1 - 1}*\text{ \lparen0.08\rparen}^0*\left(0.92\right)^3 \\ P(x\ge1)\text{ = 1 - 1}*\text{ 1 }*0.7787 \\ P(x\ge1)\text{ = 1 - 0.7787} \\ P(x\ge1)\text{ = 0.221} \end{gathered}`

Thus the required probability is 0.221.