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