courses › Probability & Statistics

“And”, “or”, and drawing without putting back.

Pen and paper is fine · no calculator needed why?

Learn first (about 3 minutes)

Opens at level 24.

Sign in to start

Builds on: Chance basics (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Independent “and” par 22 s not tried yet

  worked example

  You flip a fair coin and roll a fair six-sided die. What is the probability of heads and a multiple of 3 on the die? Give the answer as a fraction in lowest terms.

  Answer: 1/6

  1. The results don’t affect each other, so multiply: 1/2 × 2/6 = 2/12 = 1/6.

• Without replacement par 20 s not tried yet

  worked example

  A bag has 8 orange and 10 white marbles. You draw 2 marbles at random, one after another, without putting any back. What is the probability that both are orange? Give the answer as a fraction in lowest terms.

  Answer: 28/153

  1. 8/18 for the first, then 7/17 for the second: each pick leaves one fewer.
  2. 8/18 × 7/17 = 56/306 = 28/153.

• “Or” with overlap par 20 s not tried yet

  worked example

  You pick a whole number from 1 to 20 at random, each equally likely. What is the probability it is a multiple of 4 or a multiple of 10 (or both)? Give the answer as a fraction in lowest terms.

  Answer: 3/10

  1. Multiples of 4: 5. Multiples of 10: 2. Both (multiples of 20): 1.
  2. 5 + 2 − 1 = 6 of the 20 numbers, so the probability is 6/20 = 3/10.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

No rounds yet.