Answer:
I) how many student are offering both subject , if only 70 students are offering neither biology nor chemistry?
= 160 students
II) how many students are offering at least one biology and chemistry?
= 330 students
Step-by-step explanation:
I) how many student are offering both subject , if only 70 students are offering neither biology nor chemistry?
Total number of student n ( B ∪ C) = 400
Students offering biology n(B) = 300
Students offering chemistry n(C) = 190
Students not offering biology nor chemistry = 70
Students offering both biology and chemistry n ( B ∩ C) = ??
n ( B ∪ C) - Students neither offering biology nor chemistry = n(B ) + n ( C ) - n ( B ∩ C)
400 - 70 = 300 + 190 - n ( B ∩ C)
330 = 490 - n ( B ∩ C)
n ( B ∩ C) = 490 - 330
n ( B ∩ C) = 160
Therefore, students offering both Biology and Chemistry are 160 students.
II) how many students are offering at least one biology and chemistry?
n(B' ) + n ( C') + n ( B ∩ C)
n(B') = Students offering biology only
= n(B) - n ( B ∩ C)
= 300 - 160 = 140
n(C') = Students offering chemistry only
n(C) - n ( B ∩ C)
= 190 - 160
= 30
(300 - 160) + (190 - 160) + 160
140 + 30 + 160
= 330 students
