Two factories — Factory A and Factory B — design batteries to be used in mobile phones. Factory A produces 60% of all batteries, and Factory B produces the other 40%. 2% of Factory A's batteries have defects, and 4% of Factory B's batteries have defects. What is the probability that a battery is both made by Factory A and defective? *

Probability that a battery is both made by Factory A and defective is 0.012 or 1.2%.

Step-by-step explanation:

We are given that Two factories — Factory A and Factory B — design batteries to be used in mobile phones. Factory A produces 60% of all batteries, and Factory B produces the other 40%.

2% of Factory A's batteries have defects, and 4% of Factory B's batteries have defects.

Let the Probability that factory A produces batteries = P(A) = 0.60

Probability that factory B produces batteries = P(B) = 0.40

Also, let D = event that battery is defective

Probability that batteries have defects given that it is produced by Factory A = P(D/A) = 0.02

Probability that batteries have defects given that it is produced by Factory B = P(D/B) = 0.04

Now, probability that a battery is both made by Factory A and defective = Probability that factory A produces batteries Probability that batteries have defects given that it is produced by Factory A

                       =  P(A) P(D/A)

                       =  0.60 0.02 = 0.012  or  1.2%

Therefore, the probability that a battery is both made by Factory A and defective is 1.2%.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.