In a class of 30 students, 15 students study Spanish, and 3 of the Spanish students also study German.
7 students study neither Spanish nor German.
Draw a Venn diagram to show this information.
We start with the 3 in the intersection ("overlap"); we can then deduce the "Spanish only" section is 12.
7 needs to be outside both bubbles but within the box.
With a total of 30 we can work out how many students study "German only" and complete the diagram.
Use your Venn diagram to find the probability that a student, selected at random from the class, studies Spanish but not German.
Highlight the part "Spanish only".
Pick out the numbers you need carefully.
Students studying "Spanish only" = 12
Total number of students = 30
P(Spanish only)
Given the Venn diagram below, find the following probabilities:
P( A)
Draw a 'mini'-Venn diagram - a quick sketch without the details.
See these questions as "ways to win" - so in this part you win if in "bubble A".
B and C do not come into it at all.
Total in A = 3 + 5 + 1 + 8 =17
Total = 3 + 5 + 1 + 8 + 2 + 4 + 8 + 9 = 40
P( A ∩ B ∩ C )
∩ - intersection - AND - "win" if "in A" AND "in B" AND "in C".
Total in A
AND B AND C = 8
Total = 40
P( B' ∩ C )
∩ - intersection - AND - "win" if "not in B" AND "in C".
Total in "not B" AND C = 5
Total = 40
P( A ∪ B )
∪ - UNION - OR - "win" if "in A" OR "in B".
Total in A
OR B = 3 + 1 + 8 + 5 + 2 + 8 = 27
Total = 40
P( A ∪ B ∪ C )
∪ - union - OR - "win" if "in A" OR "in B" OR "in C".
In this case, it will be easier to subtract from the whole total.
Total in A OR B OR C = 40 - 9 = 31
Total = 40
P( A' ∪ B' )
∪ - union - OR - "win" if "not in A" OR "not in B".
This one is particularly difficult to see without a diagram!
Total in A'
OR B ' = 40 - 8 - 5 = 27
Total = 40