Hi tutors can you guide and help me with this. The lesson is already in the picture use this as a guide thanks for helping(some of the pictures is just a lesson)

Week 8 Find the Probability of (A U B) In the previous lesson you learned how to illustrate probability of union of two events. In this module, you are expected to find the probability of A U B. The union of events A and B, denoted by A U B, consists of all outcomes that are in A or in B or in both A and B. The intersection of events A and B, denoted by A n B , consists of all outcomes that are in both A and B. The general probability addition rule for the union of two sets states that: P(A U B) = P(A) + P(B) - P(A n B) To find the probability of an event of the union of two events, we add the probabilities of the two events and subtract the probability that both events occur simultaneously. Examples: 1. Find the probability of selecting music club or dance club using the illustration below. Music club Dance club 12 16 10 Solution: a. Find the total number of possible outcomes: N = 46 b. Find the probability of music club. P(A) = 20 _ 10 46 c. Find the probability of dance club. (B) = =4 23 d. Find the probability of both music club and dance club. P(A) = 3 = 4 46 23 e. Using the formula: P(A U B) = P(A) + P(B) - P(A n B) 10 4 12 . 4- 1 P(A U B) = 23 + 23 23 2 Therefore, the probability of selecting music club or dance club is. 2. What is the probability of getting two even or at least one two in throwing a pair of dice? a. The total number of possible outcomes: N = 36 b. The probability of getting two even: P (A) = (2-2, 4-2, 6-2, 2-4, 4-4, 6-4, 2-6, 4-6, 6-6} = = =-c. The probability of getting at least one two: P (A) = {2-1, 1-2, 2-2, 3-2, 4-2, 5-2, 6-2, 2-3, 2-4, 2-5, 2-6} = 12 d. The probability of getting both, two even or at least one two: P (A) = {2-2, 4-2, 6-2, 2-4, 2-6} = e. Using the formula: P(A U B) = P(A) + P(B) - P(A n B) P(A U B) = 2 + 11 . 5 _ 15_ 36 36 12 Therefore, the probability of getting two even or at least one two in throwing a pair of dice is 7. 3. Find the probability of landing a multiple of 2 and a factor of 8 in a number wheel. 2 8 3 6 Solution: a. The total number of possible outcomes: N = 8 b. The probability of landing a multiple of 2: P(A) = {2, 4, 6, 8) = = c. The probability of landing a factor of 8: P(B) = {1, 2, 4, 8} = = 7 d. The probability of landing both a multiple of 2 and a factor of 8: P(A) = (2, 4, 8) = e. Using the formula: P(A U B) = P(A) + P(B) - P(A n B) P(A U B) = 3+ * Therefore, the probability of landing a multiple of 2 and a factor of 8 is 18. 4. A group of teachers assigned to attend a Regional training. The ages and gender is summarized below. If one is chosen at random, find the probability that it was a female or ages 20-34. 20 - 34 34 - 48 49 - 64 Total Male 18 12 4 34 Female 24 32 10 66 Total 42 44 14 100Solution: a. The total number of possible outcomes: N = 100 b. The probability of choosing a female: P(A) = = :4: c. The probability of choosing ages 20-34: P(B) i E _ 1oo _ so d. The probability of choosing both female or ages 20-34: P(A) i E _ 1oo _ 25 e. Using the formula: P(A U B): P(A) + P(B) P(A n B) 84 21 pm U B): +-=_=_ 1m] 1m] 1m] ll] 25 0:0 Therefore, the probability that it was a female or ages 20-34 is %. Assessment A. Find the probability of the following. 1. Find the probability of not getting 3 in casting a die. 2. From a set on numbers from 1 to 10, find the probability of picking a prime number. 3. Find the probability of getting a Queen from a deck of 52 playing cards. 4. A roulette contains 3 red balls. 4 yellow balls, 8 blue balls and 5 gray balls. Find the probability ol picking a yellow ball. 5. Find the probability of getting a sum of 7 in casting a pair of dice. B. Find probability of a union of two events. 1. 150 Elementary students were interviewed about which fast-food they prepared, Jollibee or Mc Donald. The result illustrated below: Jollibee Mc Donalds s a. Find the probability of choosing Jollibee. b. Find the probability of choosing Mc Donald's. c. Find the probability of Choosing both Jollibee or Mc Donald's. d. Find P (A u B). 2. 200 students participated in a high school festival. They registered with the lollowing team: sports team, swimming team and musical team. The summarized table illustrated below: Team Team Team Total Male 32 24 30 86 Female 40 33 41 1 1 4 Total 72 57 71 200 If one participant was chosen at random, find the probability that it is, a. a male participant or from sports team. b. from a musical team and a female participant. c. a female and from swimming team. 3. A iar contains 20 balls numbered 1 to 20. If a ball was drawn randomly from a jar, find the probability of picking, a. an even number and a multiple of 4. b. a factor of 10 and divisible by 5. 4. A card is drawn from a deck of 52 playing cards. Find the Probability of the following. a. drawing a face or a heart. b. drawing a black or a club. c. drawing an ace and a spade. d. drawing a king or a red card. 9. drawing a red or a number card. 5. If a pair of dice was thrown, what is the probability of landing: a. two even and only one-four. b. at least one three and two odd numbers 0. sum of 6 and a pair of odd numbers. d. a pair of even numbers and a sum of 8. 9. sum of 9 and only one three