Question

A large chain retailer purchases an electric device from the manufacturer. The manufacturer indicates that the defective rate of the device is 10%. The inspector of the retailer randomly selects 4 items from a shipment. Complete the following activity to find the probability that the inspector finds at most one defective item in the 4 selected items.

Solution:

Here, n = 4

p = probability of defective device = 10% = `10/100 = square`

∴ q = 1 - p = 1 - 0.1 = `square`

X ∼ B(4, 0.1)

 `P(X=x)=""^n"C"_x p^x q^(n-x)= ""^4"C"_x (0.1)^x (0.9)^(4 - x)`

P[At most one defective device] = P[X ≤ 1]

= P[X=0] + P[X=1]

= `square+square`

∴ P[X ≤ 1] = `square`

Answer 1

Here, n = 4

p = probability of defective device = 10% = `10/100 = bb(0.1)`

∴ q = 1 - p = 1 - 0.1 = `bb(0.9)`

X ∼ B(4, 0.1)

 `P(X=x)=""^n"C"_x p^x q^(n-x)= ""^4"C"_x (0.1)^x (0.9)^(4 - x)`

P[At most one defective device] = P[X ≤ 1]

= P[X=0] + P[X=1]

= `bb(""^4"C"_0 (0.1)^0 (0.9)^4+""^4"C"_1 (0.1)^1 (0.9)^3)`

∴ P[X ≤ 1] = `(0.9)^3[0.9+0.4]=0.729xx1.3`

∴ P[X ≤ 1] = 0.9477