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

Answer Key - Grade 10 Math Worksheet

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

1. Read this first

   Two-way table of students

   	Wears a helmet	No helmet	Total
   Bikes	24	6	30
   Gets a ride	9	21	30
   Total	33	27	60

2. 1.

   Esme counted bikes and rides at the school gate. A student who wears a helmet is picked at random. What is the chance the student bikes to school, in simplest form?

   8/11

3. Two-way table of plants

   	Grew a flower	No flower	Total
   Sunny window	21	7	28
   Shady shelf	8	20	28
   Total	29	27	56

4. 2.

   Jun tracked the class plants for a science project. A plant that grew a flower is picked at random. What is the chance the plant is by the sunny window, in simplest form?

   21/29
5. 3.

   Kira rolls two fair number cubes in a board game. Given that the two rolls add to 8, what is the chance a roll shows 3, in simplest form?

   2/5

6. Outcome list, 25 equally likely rows (first spin, then second spin)

   1 then 1, 1 then 2, 1 then 3, 1 then 4, 1 then 5, 2 then 1, 2 then 2, 2 then 3, 2 then 4, 2 then 5, 3 then 1, 3 then 2, 3 then 3, 3 then 4, 3 then 5, 4 then 1, 4 then 2, 4 then 3, 4 then 4, 4 then 5, 5 then 1, 5 then 2, 5 then 3, 5 then 4, 5 then 5.

7. 4.

   Milo spins a spinner with 5 equal parts, numbered 1 to 5, twice. Given that the two spins add to 6, what is the chance at least one spin is odd, in simplest form?

   3/5

8. Two-way table of students

   	Grade 6	Grade 7	Total
   Plays outside	15	12	27
   Plays inside	9	14	23
   Total	24	26	50

9. 5.

   Pia made this table for the newsletter. One of the 50 students is picked at random. What is the chance the student plays inside at recess and is in grade 7, in simplest form?

   7/25

10. Two-way table of seeds

    	Sprouted	Did not sprout	Total
    Watered daily	27	3	30
    Watered weekly	12	18	30
    Total	39	21	60

11. 6.

    Ren made this table for the newsletter. One of the 60 seeds is picked at random. What is the chance it was watered daily and sprouted, in simplest form?

    9/20

12. Two-way table of tiles

    	Square	Triangle	Total
    Red	9	5	14
    Blue	12	10	22
    Total	21	15	36

13. 7.

    Ari made this table for a class project. One of the 36 tiles is picked at random. What is the chance it is a triangle, in simplest form?

    5/12

14. Two-way table of students

    	Likes puzzles	No puzzles	Total
    Grade 7	6	9	15
    Grade 8	10	15	25
    Total	16	24	40

15. 8.

    Bo surveyed students for the school paper. Does knowing that a student is in grade 7 change the chance that the student likes puzzles?

    • Yes: P(Likes puzzles | Grade 7) = 2/5 is less than 1
    • Yes: P(Grade 7 | Likes puzzles) = 3/8, not P(Likes puzzles) = 2/5
    • Yes: 6 in "Grade 7" but 10 in "Grade 8" like puzzles
    • No: P(Likes puzzles | Grade 7) = 2/5, the same as P(Likes puzzles) = 2/5
16. 9.

    Jun surveyed students for the school paper. Does knowing that a student plays chess change the chance that the student likes math?

    • No: 12 in each row like math
    • No: P(Likes math) = 1/2 is less than 1
    • Yes: P(Likes math | Plays chess) = 3/4, but P(Likes math) = 1/2
    • No: "Plays chess" and "Likes math" are about different things
17. 10.

    Kira surveyed students for the school paper. Does knowing that a student sings in choir change the chance that the student plays piano?

    • Yes: P(Plays piano | Sings in choir) = 3/5, but P(Plays piano) = 2/5
    • No: 9 in each row play piano
    • No: P(Plays piano) = 2/5 is less than 1
    • No: "Sings in choir" and "Plays piano" are about different things