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

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. Read this first

   Outcome list, 12 equally likely rows (first the cube's number, then H or T)

   1H*, 1T, 2H*, 2T, 3H*, 3T, 4H*, 4T, 5H*, 5T, 6H*, 6T. Rows where the coin shows heads are starred (*).

2. 1.

   Ari rolls a fair number cube and flips a fair coin for a board game. Given that the coin shows heads, what is the chance the cube shows more than 4, in simplest form?

   1/3
3. 2.

   HHH*, HHT*, HTH*, HTT*, THH, THT, TTH, TTT. Rows where the first coin shows heads are starred (*). Bo flips three fair coins for a board game. Given that the first coin shows heads, what is the chance exactly two coins show heads, in simplest form?

   1/2

4. Outcome list, 10 equally likely rows (one tile each)

   1, 2, 3, 4, 5*, 6*, 7*, 8*, 9*, 10*. Rows where the tile is more than 4 are starred (*).

5. 3.

   Esme picks one of ten number tiles from a bag without looking. Given that the tile is more than 4, what is the chance the tile is even, in simplest form?

   1/2

6. Outcome list, 16 equally likely rows (first spin, then second spin)

   1 then 1, 1 then 2, 1 then 3, 1 then 4, 2 then 1, 2 then 2, 2 then 3, 2 then 4*, 3 then 1, 3 then 2, 3 then 3*, 3 then 4, 4 then 1, 4 then 2*, 4 then 3, 4 then 4. Rows where the two spins add to 6 are starred (*).

7. 4.

   Kira spins a spinner with 4 equal parts, numbered 1 to 4, twice. Given that the two spins add to 6, what is the chance the second spin is even, in simplest form?

   2/3

8. Two-way table of students

   	Instrument	No instrument	Total
   Plays a sport	12	8	20
   No sport	4	16	20
   Total	16	24	40

9. 5.

   Luz made this table for a class project. Which division gives the chance that a student plays an instrument, given that the student plays a sport?

   • 12 ÷ 20
   • 20 ÷ 40
   • 12 ÷ 40
   • 12 ÷ 16

10. Two-way table of books

    	Hardcover	Paperback	Total
    Fiction	7	13	20
    Nonfiction	11	9	20
    Total	18	22	40

11. 6.

    Noah made this table for a class project. Which division gives the chance that a book is fiction, given that the book is a hardcover?

    • 7 ÷ 18
    • 7 ÷ 20
    • 18 ÷ 40
    • 7 ÷ 40

12. Two-way table of students

    	Breakfast at home	Breakfast at school	Total
    Walks	15	5	20
    Rides the bus	9	11	20
    Total	24	16	40

13. 7.

    Pia made this table for a class project. Which division gives the chance that a student eats breakfast at school, given that the student rides the bus?

    • 11 ÷ 40
    • 20 ÷ 40
    • 11 ÷ 16
    • 11 ÷ 20
14. 8.

    Ren asked students about pets for the school paper. A student who has a pet is picked at random. What is the chance the student walks to school, in simplest form?

    3/5

15. Two-way table of books

    	Hardcover	Paperback	Total
    Fiction	8	12	20
    Nonfiction	10	5	15
    Total	18	17	35

16. 9.

    Tala sorted the books on one library cart. A book that is a paperback is picked at random. What is the chance the book is fiction, in simplest form?

    12/17

17. Two-way table of members

    	Morning	Afternoon	Total
    Art club	5	15	20
    Chess club	9	11	20
    Total	14	26	40

18. 10.

    Ari sorted club members by meeting time. A member who meets in the morning is picked at random. What is the chance the member is in art club, in simplest form?

    5/14