Question

I am in some serious need of help

If P(a)=1/3, P(b)=2/5, and P(AuB)=3/5 what is P=(AnB)?

Answer 1

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


`\implies P(A\cap B)=\frac13+\frac25-\frac35=\frac2{15}`

Answer 2

The value of P=(AnB) is
`(2)/(15)`.

Explanation:

It is given that

`P(A)=(1)/(3)`

`P(B)=(2)/(5)`

`P(A\cap B)=(3)/(5)`

According to the union formula:

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

`P(A\cup B)=(1)/(3)+(2)/(5)-(3)/(5)`

`P(A\cup B)=(1)/(3)+(2-3)/(5)`

`P(A\cup B)=(1)/(3)-(1)/(5)`

`P(A\cup B)=(5-3)/(15)`

`P(A\cup B)=(2)/(15)`

Therefore the value of P=(AnB) is
`(2)/(15)`.