Respuesta :
Answer: a) 1060, b) [tex]\dfrac{61}{167}[/tex]
Step-by-step explanation:
Since we have given that
Number of boys = 870
Number of girls = 800
Probability that a boy chosen studies Spanish = [tex]\dfrac{2}{3}[/tex]
Probability that a girl chosen studies Spanish = [tex]\dfrac{3}{5}[/tex]
So, the number of boys in the school who study Spanish would be
[tex]\dfrac{2}{3}\times 870=290\times 2=580[/tex]
So, the number of girls in the school who study Spanish would be
[tex]\dfrac{3}{5}\times 800\\\\=3\times 160\\\\=480[/tex]
So, total number of students who study Spanish would be :
[tex]480+580=1060[/tex]
b) What is the probability, as a fraction in its simplest form, that a student
chosen at random from the whole school does not study Spanish?
Number of students who do not study Spanish would be:
[tex](870+800)-1060\\\\=1670-1060\\\\=610[/tex]
So, the probability of students who does not study Spanish would be :
[tex]\dfrac{610}{1670}=\dfrac{61}{167}[/tex]
Hence, a) 1060, b) [tex]\dfrac{61}{167}[/tex]
