Practice Maths

Venn Diagrams and Two-Way Tables — Solutions

Click any answer to watch the solution video.

  1. Soccer and basketball survey

    1. Venn diagram:
    2. Neither:
    3. P(soccer only):
    4. P(at least one sport):
    5. P(basketball but not soccer):

  2. Reading from a Venn diagram

    1. Sum check:
    2. P(A):
    3. P(B):
    4. P(A ∪ B):
    5. P(neither):
    6. Addition rule check:

  3. After-school activity table

    1. P(Sport):
    2. P(has pet):
    3. P(Gaming AND no pet):
    4. P(Reading OR has pet):
    5. P(has pet | Sport):

  4. Music and Art two-way table

    1. Two-way table:
    2. P(Music only):
    3. P(neither):
    4. P(Art | Music):

  5. Addition formula with P(A), P(B), P(A∪B)

    1. P(A ∩ B):
    2. P(A only):
    3. P(B only):
    4. P(neither):
    5. Mutually exclusive?:

  6. Mutually exclusive events C and D

    1. P(C ∪ D):
    2. P(C ∩ D):
    3. P(neither):
    4. Exhaustive?:
    5. C, D, E exhaustive?:

  7. Three-circle Venn diagram (TV preferences)

    1. Sum:
    2. P(watches Movies):
    3. P(exactly one category):
    4. P(at least two categories):
    5. P(M and S but not N):

  8. Gym members two-way table

    1. P(Weights):
    2. P(Female AND Classes):
    3. P(Cardio | Male):
    4. P(Male | Weights):
    5. Independence check:

  9. Team sport and instrument

    1. Number playing team sport:
    2. Number playing both:
    3. P(plays instrument):
    4. Venn diagram counts:
    5. P(instrument | sport):

  10. Medical screening test

    1. P(has disease):
    2. Sensitivity P(Positive | Disease):
    3. Specificity P(Negative | No Disease):
    4. Positive predictive value P(Disease | Positive):
    5. Should they be very worried?: