P(A β© B) = 11/15 β answer A
Step-by-step explanation:
* Lets revise the meaning of βͺ and β©
# A βͺ B means all the elements in A or B without reputation
- Ex: If A = {2 , 3 , 5} and B = {3 , 4 , 7}
β΄ A βͺ B = {2 , 3 , 4 , 5 , 7} β we don't repeat the element 3
# A β© B means all the elements in A and B
- Ex: If A = {2 , 3 , 5} and B = {3 , 4 , 7}
β΄ A β© B = {3}
- From the examples above
β΅ n(A) = 3 and n(B) = 3
β΅ n(A βͺ B) = 5
β΅ n(A β© B) = 1
β΄ n(A) + n(B) = n(A βͺ B) + n(A β© B)
* Now lets solve the problem
β΅ P(A βͺ B) = 11/15
β΅ P(x) = n(x)/total
- That means the total elements in the problem is 15 and n(A βͺ B) is 11
β΄ n(A βͺ B) = 11
β΅ P(A) = 2/3 β simplest form
- To find P(A) without simplification and you now the total is 15
Β then multiply up and down by 5
β΄ P(A) = (2Γ5)/(3Γ5) = 10/15
β΄ n(A) = 10
β΅ P(B) = 4/5 β simplest form
- To find P(B) without simplification and you now the total is 15
Β then multiply up and down by 3
β΄ P(B) = (4Γ3)/(5Γ3) = 12/15
β΄ n(B) = 12
- To find n(A β© B) use the rule above
β΅ n(A) + n(B) = n(A βͺ B) + n(A β© B)
β΅ 10 + 12 = 11 + n(A β© B) β subtract 11 from both sides
β΄ 11 = n(A β© B)
- The number of elements in A β© B is 11
β΅ P(A β© B) = n(A β© B)/total
β΄ P(A β© B) = 11/15