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?