Probabilities from Venn Diagrams

Probability & Venn Diagramsvideo

Probability & Venn diagrams

How do I find probabilities from Venn diagrams?

• If the Venn diagram shows frequencies in the region

  • Add together the frequencies in the regions you want

  • Divide by the total frequency

• If the Venn diagram shows the individual elements

  • Count the number of elements you want

  • Divide by the total number of elements

• For the Venn diagram shown below,

  • The probability of being in A  is $\frac{5}{11}$

    • There are 5 elements in A out of 11 in total

  • The probability of being in both A  and B  is $\frac{2}{11}$

    • There are 2 elements in A  and B  (the intersection)

  • The probability of being in A, but not B, is $\frac{3}{11}$

    • 3 elements are in A  but not B

• Some harder questions are not out of the total number, but out of a restricted number

  • The probability of being in B, given that you are already in A, is $\frac{2}{5}$

    • You are only interested in elements in A

    • There are 5 elements in A, out of which only 2 are also in B