Republic of the Philippines CAMARINES NORTE STATE COLLEGE F. Pimentel Avenue, Brgy. 2, Daet, Camarines Norte – 4600, Philippines COLLEGE OF ENGINEERING Name: Yr & Blk: SCORE: Date: Accomplished ACTIVITY 1 Probability Instructions: Evaluate each of the following functions. Show your COMPLETE solutions on an A4sized paper. 1 1. If the universe, 𝑈 = { , 0, 𝜋, 5, −√2 , −4} and the subsets of 𝑈 are given by 𝐴 = { 0, 𝜋, −√2 , } , 2 1 1 𝐵 = { , 5, −√2 , −4} and 𝐶 = { , − 4}, show and illustrate the Venn diagram and find: 2 2 a. 𝐴 ∩ 𝐵 b. 𝐴 ∪ 𝐵 c. (𝐴 ∪ 𝐵) ∩ 𝐶 d. 𝐵′ ∪ 𝐶′ e. 𝐴 ∩ 𝐵′ f. (𝐵 ∩ 𝐶)′ g. (𝐴 ∩ 𝐶) ∪ (𝐵 ∩ 𝐶) 2. A committee of 3 members is to be formed consisting of one representative each from labor, management and the public. If there are three possible representatives from labor, 2 from management and 4 from public, determine home many committees can be forms, using: a. Fundamental principle of counting b. Tree diagram 3. In how many ways can 5 differently colored marbles be arranged in a row? 4. In how many ways can 10 people be seated on a bench if only 4 seats are available? 5. How many 4-digit number can be forms with 10 digits 0, 1, 2, 3, …, 9 if: a. Repetitions are allowed b. Repetitions are not allowed c. The last digit must be zero and repetitions are not allowed 6. In how many ways can 7 people be seated at a round table if: a. They can sit anywhere b. Two particular people must not sit next to each other 7. In how many ways can 10 objects be split into two groups containing 4 and 6 objects respectively? 8. In how many ways can a committee of 5 people be chosen out of 9 people?