The counting principle, and are these events independent?
Grade 9 Math Worksheet
Circle the best answer, or write your answer on the line.
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?
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.
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?
Zee's lock has 3 dials with 7 symbols each. How many more codes are possible when symbols may repeat than when no symbol may repeat?
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?
Luz's lock has 3 dials, each showing 0 to 9. A new lock adds 2 more dials. By what fraction is the chance of a random correct guess multiplied?
A 4-letter code uses the letters A to G, with no letter used twice. Pia guesses one code at random. What is the chance it is right, in simplest form?
A code is 2 letters from A to E (repeats allowed), then 1 digit from 0 to 9. Tala guesses one code at random. What is the chance it is right?
Noah picks one card at random from cards numbered 1 to 20. A is “a multiple of 4” and B is “a multiple of 5”. Are A and B independent?
- Independent: 5/20 × 4/20 = 1/20, and only 20 is in both
- Not independent: multiples of 4 and 5 share the card 20
- Not independent: 5/20 + 4/20 is not 1/20
- Not independent: 1/20 is smaller than both 5/20 and 4/20
Tala picks one tile at random from tiles numbered 1 to 10. A is “a multiple of 2” and B is “a multiple of 3”. Are A and B independent?
- Independent: 2 and 3 share no factor
- Not independent: 5/10 × 3/10 = 3/20, but P(A and B) = 1/10
- Independent: 1/10 is smaller than both 5/10 and 3/10
- Independent: 5/10 and 3/10 are close to each other