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. 3.

   For a random student in Noah's club, P(bike) = 5/8 and P(bike and helmet) = 3/10. Given bike, what is the chance of helmet, in simplest form?

   12/25

4. Read this first

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

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

5. 4.

   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
6. 5.

   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
7. 6.

   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

8. Two-way table of students, counts only

   	Joins the club	Does not join
   Ninth grade	4	8
   Tenth grade	6	empty

9. 7.

   Zee's table of students has one empty cell. What number in the empty cell makes joining the club independent of the grade?

   12
10. 8.

    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. 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?

    • Yes: "plays chess" and "plays a sport" are about different things
    • 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
12. 10.

    For a random student at Luz's school, P(bikes to school) = 1/2, P(wears glasses) = 3/8 and P(both) = 1/4. Are the two events independent?

    • No: P(A) = 1/2 is not the same as P(B) = 3/8
    • No: 1/2 + 3/8 = 7/8, not 1/4
    • No: 1/2 × 3/8 = 3/16, not 1/4
    • Yes: "bikes to school" and "wears glasses" are about different things