Six jurors are to be selected from a pool of potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, of the prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They will not disclose this during the jury selection process. If jurors are selected at random from this group of , find the probability that the number of potentially prejudiced jurors among the selected jurors is exactly .

Complete question :

Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 2 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They will not disclose this during the jury selection process. If 6 jurors are selected at random from this group of 20, find the probability that the number of potentially prejudiced jurors among the 6 selected jurors is ;

a. exactly 1

b. none

c. at most 2

0.442 ; 0.479 ; 1

Step-by-step explanation:

Given:.

Total number of candidates = 20

Number of jurors to be selected = 6

Number of prejudiced jurors = 2

Required outcome / Total possible outcomes :

Using the combination formula :

nCr = n! ÷ (n-r)!r!

1.)

P(number of prejudiced jurors is exactly 1) :

[2C1 * 18C5] ÷ 20C6

(2*8568)÷ 38760

= 0.442

B.)

P(None of the jurors is prejudiced) :

[2C0 * 18C6] ÷ 20C6

(1 * 18564) ÷ 38760

= 0.479

C.)

P(at most 2 of the jurors are prejudiced)

P(x =0) + p(x = 1) + p(x = 2)

P(x = 2) :

[2C2 * 18C4] ÷ 20C6

(1 * 3060) ÷ 38760

= 0.079

P(x =0) + p(x = 1) + p(x = 2)

(0.479 + 0.442 + 0.079)

= 1

lolololkzaxio2ier286udeg

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)