Probability of randomly selected person
By John Campbell •
I would like some help with some problem i saw on a book, Given that there is 80% of a customers has a Salary account on bank (lets call this P(A)), and 50% of the customers have a saving account ( P(b) )?
- What is the chance of random selected person has both save and salary account?
- What is the chance of random selected person has save but NO salary account?
- What is the chance of random selected person has only one type of account ?
Regarding: 1 and 2, im between using the P(A).P(B) OR P(B|A) = P(A).P(B) / P(A)
$\endgroup$ 51 Answer
$\begingroup$Assuming $A$ and $B$ are independent,
- $\mathbb P(A\cap B) = \mathbb P(A)\mathbb P(B)=\frac45\cdot\frac12 = \frac25$.
- $\mathbb P(B) - \mathbb P(A\cap B) = \frac12 - \frac25 = \frac1{10}$.
- $\mathbb P(A) + \mathbb P(B) - 2\mathbb P(A\cap B) = \frac45 + \frac12 - 2\cdot\frac25 = \frac12$.
