Answer:
0.3689 ; 0.3592 ; 0.6301
Step-by-step explanation:
Spanish = S
French = F
German = G
n(S) = 37 ; n(F) = 38 ; n(G) = 21
n(SnF) = 17 ; n(SnG) = 7 ; n(FnG) = 10
n(SnFnG) = 3
n(SnF) only = 17 - 3 = 14 ;
n(SnG) only = 7 - 3 = 4 ;
n(FnG) only = 10 - 3 = 7
n(S) only = 37 - (14 + 3 + 4) = 16 ;
n(F) only = 38 - (14 + 3 + 7) = 14;
n(G) only = 21 - (7 + 3 + 4) = 7
Probability of not being in any language class :
Number of students not in any class (x)
(16+7+14+14+4+7+3+x) = 103
65 + x = 103
x = 103 - 65
x = 38
Probability, P = required outcome / Total possible outcomes
P(not in any class) = 38 / 103
= 0.3689
2.) probability of taking exactly one class :
Either Spanish or German or French
16/103 + 7/103 + 14/103 = 37/103 = 0.3592
3.) probability that atleast one of two students is taking a language class :
Probability that a student chosen is taking a language class :
Number of students taking a language class / total number of students
= 65 / 103
= 0.631
[P(takes class) * p(does not take class)] + [p(takes class) * p(takes class)]
(0.631 * 0.3689) + (0.631 * 0.631) = 0.6301
