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.

   Of 40 families on Esme's street, 15 have a cat, 20 a dog and 5 both. In simplest form, what is the chance a family picked at random has a cat or a dog?

   3/4
5. 4.

   Jun picks one card at random from cards 1 to 10. What is the chance of an even number or a number over 6?

   • 9/10
   • 7/10
   • 1/5
6. 5.

   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)?

   • 0.9
   • 0.2
   • 0.8
7. 6.

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

   • Subtracting keeps the chance below 1/2
   • They were counted in both groups
   • They cannot happen on one try
8. 7.

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

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

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

   • 1 − 1/2 = 1/2
   • 1/2 + 1/2 = 1
   • 1 − 1/4 = 3/4
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
    • 2/5
    • 3/10
11. 10.

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

    • 1.65
    • 0.65
    • 0.35