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…

Multiplication of Any Two-Digit Number with Any Two-Digit Number, Such that Their Ten's Digits are Equal, and Their One's Digits Add Up to Ten

In this Math Trick we are going to multiply any two-digit number with any two digit number, Such that their ten's digits are equal, and their one's digits add up to ten. This is represented by the formula, (10A+B) (10A 4C) = ; A = (0,1...9), B+C = 10 Just multiply the ten's digit of the mulitiplicand plus one with the ten's digit of the second number and write it down as the first and/or second digits or thousand's and/or hundred's digits of the answer, and multiply the one's digits, and write it down as the third…

The Square of Any Two-digit Number

, In this Math Trick, we are going to square any two-digit number.   It is represented by, the formula, (10X + Y) 2  = 100X2 + 20XY + Y 2 Or by Square of Binomial Method, with HTO, HundredsTensOnes (1st2nd3rd-Digits) Let's solve for, 1. 12 2 , 2. 23 2  3. 87 2 Solution: 1a. 12 2  = 100*1 2  + 20*1*2 + 2 2              = 100 + 40 + 4               = 144 1b. By Square of Binomial Method : 12 2   = 1 2  for the first digit l 1*2*2 for the second digit l 2 2         = 1 l 4 l 4         = 144 2a. 23 2  = 100*2 2  + 20*2*3 + 3 2             =…

Multiplication of Two Same-Digits Number and One-Digit Number

1. 22 x 9 = 2. 33 x 8 = 3. 44 x 7 = 4. 55 x 6 = 1. 22 x 9 = ; 2 x 9 = 18. Write 1 & 8 with one-digit apart. They will be the first and third digits of the answer. Now, for the second digit, add the first and third digits, which in this example are 1 & 8. Their sum is 9. Therefore, the answer is 198. 2. 33 x 8 = ; 3 x 8 = 24. Write 2 & 4 with one-digit apart. They will be the first and third digits of the answer. Now, for the second digit, add the first and third digits, which in this example are 2 & 4. Their sum is 6. Therefo…