Flashcards · J560 · Topic 11

Probability flashcards

14 cards on Topic 11, subtopics 11.01 to 11.02. Pick a subtopic or study them all.

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The probability scale: 0 is impossible, 0.5 evens, 1 certain. A probability is never below 0 or above 1. P(not A) = 1 − P(A).
Relative frequency: Number of times the outcome happened ÷ number of trials. It estimates the probability, and gets more reliable with more trials.
Expected number of outcomes: Probability × number of trials. It is an average, so it can be a decimal; the real result often differs.
Random compared with fair: Random: the next outcome cannot be predicted. Fair (unbiased): every outcome equally likely. A biased dice is still random.
Two fair dice: P(double) and P(total 7): There are 36 equally likely pairs. P(double) = 6/36 = 1/6. P(total 7) = 6/36 = 1/6.
Frequency tree: how do you fill in missing numbers?: Put the total in the first box. The numbers on the branches from one box add up to that box, so find missing numbers by subtracting.

Sample space for two coins: HH, HT, TH, TT: 4 equally likely outcomes. HT and TH are different outcomes.
Addition laws for P(A or B): Mutually exclusive: P(A or B) = P(A) + P(B). General: P(A or B) = P(A) + P(B) − P(A and B).
Mutually exclusive compared with independent: Mutually exclusive: cannot happen together, so P(A and B) = 0. Independent: one does not change the probability of the other, so P(A and B) = P(A) × P(B).
3 red and 5 blue discs; two taken without replacement. P(both red) and P(at least one red)?: P(both red) = 3/8 × 2/7 = 6/56 = 3/28. P(no red) = 5/8 × 4/7 = 20/56 = 5/14, so P(at least one red) = 1 − 5/14 = 9/14.
How do you fill a two-circle Venn diagram?: 1. Fill the overlap first. 2. Subtract it from each set total for the "only" parts. 3. Subtract all three from the group total for the outside. 4. Check all four regions add to the total.
Product rule: how many 4-digit PINs with no repeated digits?Higher: Multiply the choices at each stage, reducing by 1 when repeats are not allowed: 10 × 9 × 8 × 7 = 5040.
Conditional probability formulaHigher: P(A given B) = P(A and B) ÷ P(B). The denominator is the group named after "given". Example: P(B) = 0.35, P(A and B) = 0.14 → 0.14 ÷ 0.35 = 0.4.
How can you test whether A and B are independent?Higher: Check whether P(A and B) = P(A) × P(B), or equivalently P(A given B) = P(A).