Chance of "this or that": overlapping and mutually exclusive events

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   In Ari's class of 30, 12 students play soccer, 10 play piano and 4 do both. In simplest form, what is the chance a student picked at random plays soccer or piano?

   3/5

2. Read this first

   Use this

   Cards numbered 1 to 20. Multiples of 3: 3, 6, 9, 12, 15, 18 (6 cards). Multiples of 4: 4, 8, 12, 16, 20 (5 cards). In both lists: 12 (1 card).

3. 2.

   Bo draws one card at random from cards 1 to 20 (see the lists). In simplest form, what is the chance of a multiple of 3 or 4?

   1/2
4. 3.

   For Kira's events, P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.1. What is P(A or B)?

   • 0.8
   • 0.2
   • 0.9
5. 4.

   Why does Luz subtract the overlap when finding P(A or B)?

   • They were counted in both groups
   • They cannot happen on one try
   • Subtracting keeps the chance below 1/2
6. 5.

   Milo says P(even or a 2) on a fair number cube is 1/2 + 1/6 = 2/3. Agree or disagree?

   • Agree: add the chances of the two events
   • Disagree: 2 is even, so it is 1/2
   • Disagree: multiply to get 1/12
7. 6.

   Noah says P(A or B) = 0.7 + 0.6 = 1.3. Agree or disagree?

   • Agree: 1.3 means very likely
   • Agree: likely events add to 1.3
   • Disagree: a chance is at most 1
8. 7.

   Pia says 'rolling a 2' and 'rolling a 5' cannot happen on one roll. Agree or disagree?

   • Disagree: their chances are equal
   • Disagree: a cube shows both numbers
   • Agree: one roll shows one number
9. 8.

   Ren flips two fair coins. Using the opposite, what is the chance of at least one head?

   • 1 − 1/4 = 3/4
   • 1 − 1/2 = 1/2
   • 1/2 + 1/2 = 1
10. 9.

    Of Tala's 20 classmates, 8 do art, 6 do drama and 2 do both. What is the chance one does neither?

    • 3/5
    • 3/10
    • 2/5
11. 10.

    For Zee's events, P(A or B) = 0.65. What is the chance of neither A nor B?

    • 0.35
    • 0.65
    • 1.65