Revision notes
Use the “not”, “or” and “and” rules to work out probabilities of combined events quickly.
The weather report says the chance of rain on Friday is 0.3. Yusuf wants the chance that it stays dry. That — and the chance of combined events like “rain on Friday AND on Saturday” — comes from three simple rules.
Every probability is between 0 (impossible) and 1 (certain).
An event either happens or it doesn't, so P(not A) = 1 − P(A).
If P(rain) = 0.3, then P(no rain) = 1 − 0.3 = 0.7.
🔑 Key idea: P(not A) = 1 − P(A).
Events are mutually exclusive if they cannot happen at the same time, like rolling a 2 and rolling a 5 on one die.
For these, P(A or B) = P(A) + P(B). So P(2 or 5) = 16 + 16 = 26 = 13.
🔑 Key idea: OR with mutually exclusive events → ADD.
Events are independent if one does not affect the other, like tossing a coin and rolling a die.
For these, P(A and B) = P(A) × P(B). P(head and a 6) = 12 × 16 = 112.
Picking twice without replacement changes the second probability: from 3 red and 2 blue, P(red then red) = 35 × 24 = 310. For “at least one”, use 1 − P(none).
🔑 Key idea: AND with independent events → MULTIPLY. At least one = 1 − P(none).
A fair die is rolled once. Find the probability of getting a 5 OR a 6.
Step 1: Probability of each event
P(5) = 16, P(6) = 16
Step 2: Mutually exclusive → add
P(A or B) = P(A) + P(B) = 13
Why? One pick can't be both at once, so there's no overlap to worry about.
Answer: 13
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