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)

   	Soup	Salad
   Early lunch	16	19
   Late lunch	11	9

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. Two-way table of students, counts only

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

7. 5.

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

   12

8. Two-way table of plants, counts only

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

9. 6.

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

   12

10. Two-way table of students, counts only

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

11. 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
12. 8.

    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 = 1/10, not 1/5
    • Yes: "plays chess" and "plays a sport" are about different things
    • No: P(A) = 2/5 is not the same as P(B) = 1/4
    • No: 2/5 + 1/4 = 13/20, not 1/5
13. 9.

    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: 3/5 + 1/4 = 17/20, not 3/20
    • No: 3/20 is less than both chances
    • No: P(A) = 3/5 is not the same as P(B) = 1/4
    • Yes: 3/5 × 1/4 = 3/20
14. 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?

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