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Complements, trees and two-event outcomes
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Complements, trees and two-event outcomes
Complements, trees and two-event outcomes
Example 1
P(rain)=104. Find P(no rain).
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Answer: 53
- Complement probabilities add to 1:1−104=53.
Example 2
A fair coin is tossed twice. What is the probability of exactly one head?
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Answer: 21
- The four equally likely outcomes are HH, HT, TH and TT. HT and TH each contain exactly one head, giving 42=21.
Example 3
Represent two independent coin tosses with a tree. Each branch has probability 21. How do you calculate P(H then T) along its path?
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Answer: Multiply the two branch probabilities
- For the single path H then T, multiply 21×21=41. Add probabilities only when combining distinct paths.
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