Probability

Probability is the measure of the likelihood that an event will occur. It is defined as the ratio of favorable outcomes to total possible outcomes, ranging from 0 (impossible) to 1 (certain). The addition rule (P(A∪B) = P(A) + P(B) - P(A∩B)) and multiplication rule (P(A∩B) = P(A) × P(B|A)) are fundamental. Conditional probability (P(A|B) = P(A∩B)/P(B)) is used in dependent events. Bayes' theorem relates conditional probabilities.

Governing FormulaP(A) = n(A)/n(S), P(A|B) = P(A∩B)/P(B), Bayes: P(A|B) = P(B|A)×P(A)/P(B)

Knowledge Check

10 Questions

1.A fair six-sided die is rolled once. What is the probability of rolling an even number?

2.Two coins are tossed simultaneously. What is the probability of getting exactly one head?

3.A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart?

4.If P(A) = 0.4 and P(B) = 0.3, and A and B are mutually exclusive, what is P(A∪B)?

5.A bag contains 3 red balls and 5 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

6.What is the probability of rolling a sum of 7 with two dice?

7.If P(A|B) = 0.5, P(B) = 0.4, and P(A) = 0.3, what is P(A∩B)?

8.Bayes' theorem is used to calculate:

9.Two events are independent if:

10.A box contains 6 red, 4 blue, and 2 green marbles. One marble is drawn at random. What is the probability that it is not blue?