Probability

Traps in Probability

• Assumes categories are equally likely
  Probability depends on how many of EACH there are, not how many types. Count items, not categories.
• Adds probabilities for "and" events
  "AND" for independent events → multiply. "OR" for mutually exclusive events → add. Probabilities of "both" get smaller, never bigger.
• Gives the probability of the other outcome
  Underline what is asked. P(A) = favourable ÷ total. P(not A) = 1 − P(A).
• Treats one part of a ratio as the total
  In a : b, total parts = a + b. One part = amount ÷ (a + b). Then multiply by the part you need.
• Calculates a different quantity
  Name the quantity and its unit before you start (remainder; horizontal distance; cm²). After calculating, check your number is that quantity and not a neighbour.
• Stops one step short of the answer
  Before writing the answer, re-read the question's last words (each angle? neither? Ama's share? variance?). Ask: is my number that thing, or a stage on the way to it?
• Treats 'without replacement' as 'with replacement'
  After each draw without replacement, both the number of that colour and the total go down by one: 3/10 × 2/9.
• Adds probabilities for 'and'
  'And' (both happen) → multiply. 'Or' (mutually exclusive) → add. The answer to an 'and' question must be smaller than each single probability.
• Uses only part of the information
  Tick off every number and every condition in the stem as you use it. If one is unticked at the end, the answer is incomplete.