An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 21 in the French class, and 12 in the German class. There are 9 in both Spanish and French, 5 in both Spanish and German, and 5 that are in both French and German. There are 3 students taking all 3 classes. Required:
a. If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
b. If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
c. If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?

0.55 ; 0.32 ; 0.7

Step-by-step explanation:

Let :

Spanish = S ; French = F ; German = G

SnFnG = 3

(SnF) only = 9 - 3 = 6

(SnG) only = 5 - 3 = 2

(FnG) only = 5 - 3 = 2

S only = 28 - (6+3+2) = 17

F only = 21 - (2+3+2) = 14

G only = 12 - (6+3+2) = 1

Student not taking any of the classes :

(100 - (17+14+1+2+2+6+3))

100 - 45 = 55

A.) P(not taking any language class).

Required outcome = 55

Total possible outcomes = 100

= 55 / 100 = 0.55

B.)

P(taking exactly one language class)

(S only + F only + G only) / 100

(17 + 14 + 1) / 100

= 32/100

= 0.32

C.)

Atleast 1 is taking a language class out of 2 selected

Possibilities :

(taking and not taking) ;

(not taking and taking) ;

(taking and taking)

(45/100 * 55/99) + (55/100 * 45/99) + (45/100 * 44/99) = 0.7

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you