The counting principle, and are these events independent?

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Jun's lock has 4 places with the same number of symbols s in every place. The lock has 1,296 codes. How many symbols are in each place?

   6
2. 2.

   Esme's mailbox code has 6 places with the same number of symbols s in every place. The mailbox has 729 codes. How many symbols are in each place?

   3
3. 3.

   A tree's first level has 4 ends, and every end splits into 4 new ends on each next level. Pia wants to know how many ends level 5 has.

   1024
4. 4.

   A club with n members picks a president and a different treasurer, so it has n(n − 1) ways. How many more ways are there when Ren's club grows from 12 to 15 members?

   78
5. 5.

   Kira's 3-digit code uses the digits 1 to 7, with no digit used twice, and the code must be even. How many codes are possible?

   90
6. 6.

   A 4-letter code uses the letters A to H, with no letter used twice, and must start with a vowel (A or E). Milo counts the codes. How many are possible?

   420
7. 7.

   Ari's 3-digit code uses digits 0 to 9 with no digit repeated, and the first digit is not 0. Ari guesses one code at random. What is the chance it is right?

   1/648
8. 8.

   Esme shuffles cards numbered 1 to 5 and draws two without looking; the first is not put back. A is “first is even” and B is “second is even”. Are A and B independent?

   • Not independent: 8/20 × 8/20 = 4/25, but P(A and B) = 2/20
   • Independent: each draw is even 2 of 5 times, so P(A and B) = 4/25
   • Independent: the two draws are different cards
   • Independent: P(A) and P(B) are equal
9. 9.

   Jun draws 2 marbles at random from 3 red and 2 blue, not putting the first back. A is “first is red” and B is “second is red”. Are A and B independent?

   • Independent: 3/10 is close to 9/25
   • Not independent: 12/20 × 12/20 = 9/25, but P(A and B) = 6/20
   • Independent: each draw is red 3 of 5 times, so P(A and B) = 9/25
   • Independent: P(A) and P(B) are equal
10. 10.

    Ren's spinner has 12 equal parts numbered 1 to 12. A is “a multiple of 3” and B is “an even number”. Are A and B independent?

    • Independent: 4/12 × 6/12 = 2/12, and 6 and 12 are in both
    • Not independent: 4/12 and 6/12 are not equal
    • Not independent: 4/12 + 6/12 is not 2/12
    • Not independent: 6 and 12 are both multiples of 3 and even