Solving Problems Involving Union and Intersection of Two Events Using Venn Diagram

In this topic, we have to define first Cardinality as it is very much involved. Cardinality The number of elements in a given event. It is denoted by the symbol n. "Cardinality of event A" is written as n(A). Sample Problems: 1. Forty people are asked about the social media accounts that they have. How many people have: a. Facebook or Instagram accounts? n (FUI) = 8 + 7 + 5 + 2 + 4 + 3 n (FUl) = 29 b. Twitter and Instagram accounts?  n (Tnl) = 2 + 4 n (Tnl) = 6 c. Facebook or Twitter accounts? n(FUT)= 8 + 7+ 5 +2+ 4 + 6 n(FUT)= 32 …

Probability of Dependent & Independent Events

To better understand the concept and definition of Dependent and Independent Events, consider these some examples. DEPENDENT EVENTS 1 studying hard, getting a high grade 2. eating a lot, gaining weight 3. playing computer games, submitting all assignments and projects on time INDEPENDENT EVENTS 4 tossinga coin, rolling a die and getting a 6 5. attending a singing lesson, raining today Now, here are the definitions: DEPENDENT EVENTS - the result of one event affects the result of the other event. INDEPENDENT EVENTS - the occurrence of one eve…

Probability of the Union of Non- Mutually Exclusive Events

The probability of the union of two events A and B written as P(A U B) or P(A or B) is equal to sum of the probability of event A, P(A) and the probability of event B, P(B) minus the probability of events A and B occurring together (P(A ∩ B). In symbols, P(A U B) = P(A) + P(B) - P(A ∩ B) Example 1: If a card is drawn from an ordinary deck of 52 cards, find the probability of getting a heart or a face card? P(A U B) = P(A) + P(B) - P(A ∩ B) P(heart or face card) = P(heart) + P(face card) – P(heart n face card) P(heart)= 13/52 Pface card) = 12…

Probability of the Union of Mutually Exclusive Events

When two events (call them "A" and "B") are Mutually Exclusive. It is impossible for them to happen together: P(A and B) = 0 "The probability of A and B together equals 0 (impossible)" The probability of A or B is the sum of the individual probabilities: P(A U B) = P(A) + P(B) Example1: What is the probability of drawing a queen or a king on an ordinary deck of cards? P(queen or king) = P(queen) + P(king) P(queen) = 13/52 = 1/4 P(king) = 13/52 = 1/4 P(queen or king) = 1/13 + 1/14  = 2/13 Example 2: A bag contain…