Question

Among 1000 students survey, the results show that 52% are enrolled in chemistry, 45 % are enrolled in Foreign language and 60% enrolled in biology. In addition 25% enrolled in both chem and foreign language, 28 % enrolled in both biology and foreign language and 30% enrolled in both chemistry and biology while 6 % did not enroll in any of 3 subjects.
How many students enrolled in 3 subjects?
Find the number of students who enrolled in only one subject
Find the number of students who enrolled in at least 2 of 3 subjects

Answer 1

$P(B\cup C\cup F)=1-P(B^c\cap C^c\cap F^c)=1-0.06=0.94$

$P(B\cup C\cup F)=P(B)+P( C)+P(F)-P(B\cap C)-P(B\cap F)-P(F\cap C)+P(B\cap C\cap F)$

$0.94=0.6+0.52+0.45-0.3-0.28-0.25+P(B\cap C\cap F)$

$$P(B\cap C\cap F)=0.2$$

The number of students enrolled in 3 subjects:

$$1000(0.2)=200$$

The number of students who enrolled in only one subject:

$1000((0.6-0.3-0.28+0.2)+(0.52-0.3-0.25+0.2)+(0.45-0.25-0.28+0.2))=510$

The number of students who enrolled in at least 2 of 3 subjects:

$$940-510=430$$