Respuesta :
Answer:
(a) Probability that a randomly selected student is taking Spanish given that he or she is taking French = 0.5 .
(b) Probability that a randomly selected student is not taking French given that he or she is not taking Spanish = 0.6 .
Step-by-step explanation:
We are given that an elementary school is offering 2 language classes ;
Spanish Language is denoted by S and French language is denoted by F.
Also we are given, P(S) = 0.5 {Probability of students taking Spanish language}
P(F) = 0.4 {Probability of students taking French language}
[tex]P(S\bigcup F)[/tex] = 0.7 {Probability of students taking Spanish or French Language}
We know that, [tex]P(A\bigcup B)[/tex] = [tex]P(A) + P(B) -[/tex] [tex]P(A\bigcap B)[/tex]
So, [tex]P(S\bigcap F)[/tex] = [tex]P(S) + P(F) - P(S\bigcup F)[/tex] = 0.5 + 0.4 - 0.7 = 0.2
[tex]P(S\bigcap F)[/tex] means Probability of students taking both Spanish and French Language.
Also, P(S)' = 1 - P(S) = 1 - 0.5 = 0.5
P(F)' = 1 - P(F) = 1 - 0.4 = 0.6
[tex]P(S'\bigcap F')[/tex] = 1 - [tex]P(S\bigcup F)[/tex] = 1 - 0.7 = 0.3
(a) Probability that a randomly selected student is taking Spanish given that he or she is taking French is given by P(S/F);
P(S/F) = [tex]\frac{P(S\bigcap F)}{P(F)}[/tex] = [tex]\frac{0.2}{0.4}[/tex] = 0.5
(b) Probability that a randomly selected student is not taking French given that he or she is not taking Spanish is given by P(F'/S');
P(F'/S') = [tex]\frac{P(S'\bigcap F')}{P(S')}[/tex] = [tex]\frac{1- P(S\bigcup F)}{1-P(S)}[/tex] = [tex]\frac{0.3}{0.5}[/tex] = 0.6 .
Note: 2. A pair of fair dice is rolled until a sum of either 5 or 7 appears ; This question is incomplete please provide with complete detail.
