Question

Please help!

P(A) = 1/3
P(B) = 2/9
P(A U B) = 4/9
Find P(A ∩ B).
A. 1
B. 1/3
C. 1/9
D. 20/18

Answer 1

`\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)`

`\\ \rm\leadsto P(A\cap B)=(1)/(3)+(2)/(9)-(4)/(9)`

`\\ \rm\leadsto P(A\cap B)=(3+2-4)/(9)`

`\\ \rm\leadsto P(A\cap B)=(1)/(9)`

Answer 2

`\sf C. \quad (1)/(9)`

Explanation:

Addition Law for Probability

`\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)`

Given:

`\sf P(A)=(1)/(3)=(3)/(9)`

`\sf P(B)=(2)/(9)`

`\sf P(A \cup B)=(4)/(9)`

Substitute the given values into the formula and solve for P(A ∩ B):

`\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)`

`\implies \sf (4)/(9) = \sf (3)/(9)+(2)/(9)-P(A \cap B)`

`\implies \sf P(A \cap B) = \sf (3)/(9)+(2)/(9)-(4)/(9)`

`\implies \sf P(A \cap B) = \sf (3+2-4)/(9)`

`\implies \sf P(A \cap B) = \sf (1)/(9)`