20% of the applicants for a certain sales position are fluent in both Chinese and Spanish. Suppose that four jobs requiring fluency in Chinese and Spanish are open. Find the probability that two unqualified applicants are interviewed before finding the fourth qualified applicant, if the applicants are interviewed sequentially and at random.

The probability that two unqualified applicants are interviewed before finding the fourth qualified applicant = 0.164

Step-by-step explanation:

Let,

The number of unqualified applicants are interviewed before finding the fourth qualified applicant = x

So,

X be the negative Binomial (n = 4 , P = )

As , we know that

P(X = n ) = ⁿ⁺⁴⁻¹Cₙ × (1 - 0.2 )⁴ × (0.2)ⁿ  for n = 0, 1, 2, ....

As we have to find the probability that two unqualified applicants are interviewed before finding the fourth qualified applicant

⇒n = 2

∴

P(X = 2 ) = ²⁺⁴⁻¹C₂ × (1 - 0.2 )⁴ × (0.2)²  for n = 0, 1, 2, ....

               = ⁵C₂ × (0.8 )⁴ × (0.2)²  

               = × 0.41 × 0.04

               = × 0.0164

               = × 0.0164

               = 10 × 0.0164 = 0.164

∴ we get

The probability that two unqualified applicants are interviewed before finding the fourth qualified applicant = 0.164

The answer is in the image 

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The answer is in the image 

The solution is given in the image below

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.