UCAT independent and dependent events
Independent: multiply the probabilities. Without replacement: after the first pick, take one away from the top and the bottom. At least one: 1 minus the chance of none. Try two below.
Decision Making · Question 1 of 20:00 / 1:03
A bag contains 8 red and 10 blue counters. Two counters are selected at random without replacement. What is the probability that both are red, to one decimal place?
Worked answers
1. A bag contains 8 red and 10 blue counters. Two counters are selected at random without replacement. What is the probability that both are red, to one decimal place?
Answer: B: 18.3%
- First red probability = 8/18.
- Second red after a red = 7/17.
- Both red = 8/18 × 7/17 = 18.3%.
2. Three independent checks each have a 18% chance of identifying a fault. What is the probability that at least one identifies it, to one decimal place?
Answer: B: 44.9%
- No check identifies it = 0.82³.
- At least one identifies it = 1 − 0.551368 = 44.9%.
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Three rules
| Situation | Do this | Example |
|---|---|---|
| Both happen, independent | Multiply | 0.6 × 0.6 = 0.36 |
| Without replacement | Change the second fraction | 8/18 × 7/17 |
| At least one | 1 − P(none) | 1 − 0.82³ = 0.449 |
The trap
Adding probabilities for "at least one" goes wrong: three 40% chances do not make 120%. Work out none, then subtract from 1.
Keep going
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