Question

in a box of 250 parts there are 5 defective parts. if 3 parts are randomly pulled from the box without replacement, what is the probability all 3 parts will be defective?

Answer 1

Answer: 1/257300

Explanation:

Let S= total number of sample space

Let D= defective parts

Let ND= Non- defective parts

Let Pr(D) = probability of defective parts in the box

Let Pr(ND) = PROBABILITY OF non-defective parts

S= 250

D = 5

ND= 250 – 5

= 245

Pr(D) =5/250

= 1/50

Pr(ND) = 245/250

= 49/50

The probability of picking 3 parts that will be defective without replacement is

Pr(D₁) n Pr(D₂) n Pr(D₃)

Pr(D₁) = 5/250

Pr(D₂) = 4/249

Pr(D₃) = 3/248

= 5/250 × 4/249 × 3/248

= 60/15438000

= 1/257300