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

   	Grade 7	Grade 8	Total
   Likes music	18	12	30
   Likes art	14	21	35
   Total	32	33	65

2. 1.

   Bo surveyed students about favorite classes. A student who likes art class is picked at random. What is the chance the student is in grade 7, in simplest form?

   2/5
3. 2.

   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

4. 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

5. 3.

   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
6. 4.

   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
7. 5.

   HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT. Luz flips four fair coins. Given that at least three coins show heads, what is the chance the first coin shows heads, in simplest form?

   4/5

8. Two-way table of seeds

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

9. 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

10. Two-way table of students

    	Wants a field trip	Wants a movie day	Total
    Grade 6	14	6	20
    Grade 7	16	12	28
    Total	30	18	48

11. 7.

    Tala made this table for a class project. One of the 48 students is picked at random. What is the chance the student wants a field trip, in simplest form?

    5/8
12. 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: 6 in "Grade 7" but 10 in "Grade 8" like puzzles
    • Yes: P(Likes puzzles | Grade 7) = 2/5 is less than 1
    • No: P(Likes puzzles | Grade 7) = 2/5, the same as P(Likes puzzles) = 2/5
    • Yes: P(Grade 7 | Likes puzzles) = 3/8, not P(Likes puzzles) = 2/5
13. 9.

    Esme surveyed students for the school paper. Does knowing that a student bikes to school change the chance that the student eats breakfast?

    • Yes: 8 in "Bikes" but 14 in "Walks" eat breakfast
    • Yes: P(Bikes | Eats breakfast) = 4/11, not P(Eats breakfast) = 2/3
    • Yes: P(Eats breakfast | Bikes) = 2/3 is less than 1
    • No: P(Eats breakfast | Bikes) = 2/3, the same as P(Eats breakfast) = 2/3
14. 10.

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

    • No: "Sings in choir" and "Plays piano" are about different things
    • 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