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. 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.

9. 6.

   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

10. Two-way table of students

    	Reads daily	Reads weekly	Total
    Has a library card	16	14	30
    No card	4	6	10
    Total	20	20	40

11. 7.

    Noah made this table for the newsletter. One of the 40 students is picked at random. What is the chance the student has a library card and reads every day, in simplest form?

    2/5

12. Two-way table of seeds

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

13. 8.

    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

14. 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

15. 9.

    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
16. 10.

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