Conditional probability, from outcomes or from a two-way table, and what it says about independence

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   For a random student in Luz's club, P(sport) = 3/5 and P(sport and instrument) = 1/4. Given sport, what is the chance of instrument, in simplest form?

   5/12
2. 2.

   For a random student in Milo's club, P(pet) = 2/3 and P(pet and garden) = 1/6. Given pet, what is the chance of garden, in simplest form?

   1/4

3. Read this first

   Two-way table of students, counts only (no totals)

   	Grade 9	Grade 10
   Swims	13	17
   Does not swim	22	8

4. 3.

   Pia asked students about the swim unit. A student who is in grade 10 is picked at random. What is the chance the student swims, in simplest form?

   17/25
5. 4.

   Ren counted lunch choices at the school cafe. A student who has late lunch is picked at random. What is the chance the student picks soup, in simplest form?

   11/20
6. 5.

   Tala asked students how they get around. A student who lives far from school is picked at random. What is the chance the student owns no scooter, in simplest form?

   19/25

7. Two-way table of plants, counts only

   	Flowered	Did not flower
   Sunny window	14	21
   Shady shelf	8	empty

8. 6.

   Ari's table of plants has one empty cell. What number in the empty cell makes flowering independent of the spot?

   12

9. Two-way table of students, counts only

   	Passed the swim test	Not yet
   Morning class	12	4
   Afternoon class	15	empty

10. 7.

    Bo's table of students has one empty cell. What number in the empty cell makes passing the swim test independent of the class time?

    5
11. 8.

    For a random student at Esme's school, P(walks to school) = 1/3, P(has a pet) = 3/5 and P(both) = 1/5. Are the two events independent?

    • No: 1/5 is less than both chances
    • Yes: 1/3 × 3/5 = 1/5
    • No: P(A) = 1/3 is not the same as P(B) = 3/5
    • No: 1/3 + 3/5 = 14/15, not 1/5
12. 9.

    For a random student at Jun's school, P(plays chess) = 2/5, P(plays a sport) = 1/4 and P(both) = 1/5. Are the two events independent?

    • No: 2/5 + 1/4 = 13/20, not 1/5
    • No: P(A) = 2/5 is not the same as P(B) = 1/4
    • No: 2/5 × 1/4 = 1/10, not 1/5
    • Yes: "plays chess" and "plays a sport" are about different things
13. 10.

    For a random student at Kira's school, P(eats lunch at school) = 3/5, P(is in band) = 1/4 and P(both) = 3/20. Are the two events independent?

    • No: P(A) = 3/5 is not the same as P(B) = 1/4
    • Yes: 3/5 × 1/4 = 3/20
    • No: 3/5 + 1/4 = 17/20, not 3/20
    • No: 3/20 is less than both chances