union | MathCelebrity Forum

# union

1. ### Prove P(A’) = 1 - P(A)

Prove P(A’) = 1 - P(A) The sample space S contains an Event A and everything not A, called A' We know P(S) = 1 P(S) = P(A U A') P(A U A') = 1 P(A) + P(A') = 1 subtract P(A) from each side: P(A’) = 1 - P(A)
2. ### A={2,3} B={4,5} find a union b

A={2,3} B={4,5} find a union b A union B is everything in A and B A U B = {2, 3, 4, 5}
3. ### In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like either tea or coffee We don't want to count duplicates, so we have the following formula Tea Or Coffee = Tea + Coffee - Both Tea Or Coffee = 40 + 30 - 10 Tea Or...
4. ### 52% of a town's households have children and 25% have pets. If 12% have both, what percent have neit

52% of a town's households have children and 25% have pets. If 12% have both, what percent have neither Let C represent households with children. Let P represents households with pets. We have the formula to determine households with Children or Pets as C U P (C Union P) or (C or P): C U P = C...
5. ### If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is

If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is We know that: n(AUB) = n(A) + n(B) - n(AintersectionB) Plugging in our given numbers, we get: n(AUB) = 1200 + 1250 - 320 n(AUB) = 2130
6. ### Let A={a,b,c} and B={1,2,3} Compute A∪B

Let A={a,b,c} and B={1,2,3} Compute A∪B Union means all elements in either A or B, so we have: A∪B = {a,b,c,1,2,3}
7. ### (A intersection B) U (A intersection B')

(A intersection B) U (A intersection B') This is the Universal Set U. Everything that isn't A and isn't B is everything else.
8. ### There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 5

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 56 people use the track. 38 people use the gym and the pool. 31 people use the pool and the track. 33 people use the gym and the track. 16 people use all three facilities. A person is selected...
9. ### 45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many s

45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many students are not taking either? Let S be the number of students taking spanish and C be the number of students taking chemistry: We have the following equation relating unions and intersections...
10. ### If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B)=

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B)=? We know the following formula for the probability of 2 events: P(A U B) = P(A) + P(B) - P(A intersection B) We're told A and B are independent, which makes P(A intersection B) = 0. So we're left with: P(A U B) =...
11. ### Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both?

Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both? Let T be tea drinkers Let C be coffee drinkers Let (T & C) be Tea & Coffee drinkers. And 53 are total. So we use the Union formula relation: C U T = C + T - (C & T) 53 = 18 + 36 - (C & T) C & T = 53 - (Not...
12. ### A = { 0 , 2 , 4 , 6 , 8 } B = { 0 , 1 , 2 , 3 , 4 , 5 , 6 } C = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } Find

A = { 0 , 2 , 4 , 6 , 8 } B = { 0 , 1 , 2 , 3 , 4 , 5 , 6 } C = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } Find ( A ∪ B ) ∩ C A U B is everything in A and B A U B = {0, 1, 2, 3, 4, 5, 6, 8} ( A ∪ B ) ∩ C means everything in both ( A ∪ B ) and C ( A ∪ B ) ∩ C = {4, 5, 6, 8}
13. ### 26 students 15 like vanilla 16 like chocolate. 3 do not like either flavour. How many like both vani

26 students 15 like vanilla 16 like chocolate. 3 do not like either flavour. How many like both vanilla and chocolate Define our people: We have Vanilla Only Chocolate Only Both Vanilla and Chocolate Neither Vanilla Nor Chocolate Add up 1-4 to get our total Total = Vanilla Only + Chocolate...
14. ### All real numbers that are less than equal to -1 or greater than 5

We have two expressions here, so we need a union since we have the word or. First, All real numbers less than or equal to -1 is x <= -1. All real numbers greater than 5 is x > 5 So we have x <= -1 U x > 5