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. 1.

   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
2. 2.

   RR*, RB*, RG*, BR, BB, BG, GR, GB, GG. Rows where the first spin is red are starred (*). Jun spins a spinner with equal red, blue and green parts twice. Given that the first spin is red, what is the chance at least one spin is blue, in simplest form?

   1/3

3. Read this first

   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 (*).

4. 3.

   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

5. Two-way table of students

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

6. 4.

   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 ÷ 16
   • 12 ÷ 40
7. 5.

   Milo made this table for a class project. Which division gives the chance that a student is in grade 7, given that the student likes dogs best?

   • 5 ÷ 15
   • 5 ÷ 14
   • 5 ÷ 30
   • 14 ÷ 30

8. Two-way table of books

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

9. 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 ÷ 20
   • 18 ÷ 40
   • 7 ÷ 18
   • 7 ÷ 40

10. Two-way table of students

    	Walks	Bus	Total
    Has a pet	9	6	15
    No pet	7	8	15
    Total	16	14	30

11. 7.

    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

12. Two-way table of books

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

13. 8.

    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

14. Two-way table of students

    	Brings lunch	Buys lunch	Total
    6th grade	14	10	24
    7th grade	6	10	16
    Total	20	20	40

15. 9.

    Zee counted lunches at two tables. A student who is in 7th grade is picked at random. What is the chance the student buys lunch, in simplest form?

    5/8

16. Two-way table of members

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

17. 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