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.

   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
4. 3.

   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

5. 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

6. 4.

   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
7. 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

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.

    Zee made this table for a class project. One of the 50 students is picked at random. What is the chance the student is an only child, in simplest form?

    2/5

13. Two-way table of tiles

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

14. 9.

    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

15. Two-way table of students

    	Plays piano	No piano	Total
    Sings in choir	9	6	15
    No choir	9	21	30
    Total	18	27	45

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