courses › Business Stats & Decisions

Complements, 'both', 'at least one', and when you can't just multiply.

In your head, jot if needed · no calculator why?

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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.

• The chance it doesn't happen par 9 s not tried yet

  worked example

  A shipment has a 9% chance of arriving late. What is the chance it doesn't arrive late?

  Answer: 91%

  1. It either happens or it doesn't: 100% − 9% = 91%.

• Both happen par 16 s not tried yet

  worked example

  Two machines each run a full shift without a breakdown 90% of the time, independently of each other. What is the chance both run a full shift without a breakdown?

  Answer: 81%

  1. For independent events, multiply: 0.9 × 0.9 = 0.81, which is 81%.

• At least one par 19 s not tried yet

  worked example

  You submit two independent bids, each with a 30% chance of winning. What is the chance of winning at least one?

  Answer: 51%

  1. Chance of winning none = 0.7² = 0.49.
  2. At least one = 1 − 0.49 = 0.51, which is 51%.

• Can you just multiply? par 17 s not tried yet

  worked example

  Two clients funded by the same investor each have a 5% chance of losing their funding this year. Is 0.25% a safe estimate that both lose funding?

  1. Yes — probabilities always multiply
  2. No — you must add the two chances
  3. No — a shared risk can make both happen together
  4. Yes — just multiply the two chances

  Answer: No — a shared risk can make both happen together

  1. Multiplying 5% × 5% = 0.25% assumes the two are independent.
  2. If the investor pulls back, both can lose funding at once, so the chance that both lose funding can be much higher than 0.25%.

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

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