Question

let a and b be two events with the following probabilities.

• p(a) = 0.5
• p(b) = 0.2
• p(a and b) = 0.1

complete the sentence.
since p(a and b) equal to p(a)·p(b), events a and b must independent.

Explanation:

Step1: Calculate $P(A)\cdot P(B)$

$P(A)\cdot P(B)=0.5\times0.2 = 0.1$

Step2: Compare with $P(A\ and\ B)$

We know $P(A\ and\ B)=0.1$. Since $P(A)\cdot P(B)=0.1$ and $P(A\ and\ B) = 0.1$, we have $P(A\ and\ B)=P(A)\cdot P(B)$.

Answer:

is; be