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.

   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

4. 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.

5. 3.

   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

6. 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

7. 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
8. 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
9. 6.

   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
10. 7.

    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
11. 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: 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
    • Yes: P(Likes puzzles | Grade 7) = 2/5 is less than 1
    • Yes: 6 in "Grade 7" but 10 in "Grade 8" like puzzles
12. 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(Eats breakfast | Bikes) = 2/3 is less than 1
    • No: P(Eats breakfast | Bikes) = 2/3, the same as P(Eats breakfast) = 2/3
    • Yes: P(Bikes | Eats breakfast) = 4/11, not P(Eats breakfast) = 2/3
13. 10.

    Jun surveyed students for the school paper. Does knowing that a student plays chess change the chance that the student likes math?

    • No: "Plays chess" and "Likes math" are about different things
    • No: 12 in each row like math
    • No: P(Likes math) = 1/2 is less than 1
    • Yes: P(Likes math | Plays chess) = 3/4, but P(Likes math) = 1/2