Acompany produces a certain product, and each unit of this product may have 3 different types of defects. let di, d2,ds represent the three different kinds of defects.

suppose further that for each unit produced p(d) = .07 p(d) = .12 p(ds) = .05 p(d, u ds) = .14 p(din d2nds) = .01

(a) what is the probability that a unit does not have a type 1 defect?

(b) what is the probability that a unit has both a type 2 and 3 defect?

(c) what is the probability that a unit has both a type 2 and 3 defect, but not a type 1 defect?

(d) what is the probability that a unit has at most two defects?

Complete Question

The complete question is shown on the first uploaded image

a) 0.88

b) 0.02

c) 0.01

d) 0.99

Step-by-step explanation:

Step one: State the given parameters

Step 2 : Obtain the probability that a unit does not have a type 1 defect

          =  

                    =

                    = 0.88  

Step 3 : Obtain the probability that a unit has both type 2 and 3 defect?

          The probability of the unit having both type 2 and type 3 defect is denoted as

   This is calculated as

                    =   0.02

Therefore P(D_{2} n D_{3} ) = 0.02

Step 4 : Obtain the probability that the unit has both a type 2 and type 3 ,but not a type 1 defect

                  Let denote the  probability that the unit has both a type 2 and type 3 ,but not a type 1 defect.

This can be calculated as follows :

                                               =   0.02 - 0.01

                                               =  0.01

Step 4 : Obtain the probability that a unit has at most two defects

               P(at most 2 defects)  = 1 - P(all three defects)

                                                  =

                                                  =  1 - 0.01

                                                  = 0.99

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

answer: h

step-by-step explanation: