Probability Summary
- P(A) = n(A)/n(U) (when all outcomes are equally likely)
- Addition theorem: P(A∪B)=P(A)+P(B)−P(A∩B)
- Complementary event: P(Ā)=1−P(A)
- Repeated trials: nCk×p^k×(1−p)^(n−k)
- Conditional probability: P(A|B)=P(A∩B)/P(B)
- Expected value: E(X)=Σxi×P(xi)
Comprehensive Practice Problems
- What is the probability that the sum is 7 when a die is rolled twice?
- What is the probability of getting exactly 4 heads when a coin is tossed 6 times?
- When X∼B(8,1/4), find E(X) and V(X).
Answers
- (1,6)(2,5)(3,4)(4,3)(5,2)(6,1): 6 outcomes → 6/36=1/6
- 6C4×(1/2)^6=15/64
- E(X)=2、V(X)=3/2