Is a probability function in $\Omega{(a1, a2, a3)}$, find $P(a1)$ whether $P({a2, a3}) = 2P(a1)$.
I know that $1 = a1 + a2 + a3$.
from where I have to start ?
Is a probability function in $\Omega{(a1, a2, a3)}$, find $P(a1)$ whether $P({a2, a3}) = 2P(a1)$.
I know that $1 = a1 + a2 + a3$.
from where I have to start ?
Start by using additivity: $P(\{a_2, a_3\} \cup \{a_1\}) = P(\{a_2,a_3\})+P(\{a_1\})$. Since $\{a_2, a_3\} \cup \{a_1\} = \Omega$, and $P(\Omega) = 1$, we have found that $ P(\{a_2,a_3\})+P(\{a_1\}) = 1.$ Now substitute $P(\{a_2,a_3\}) = 2P(\{a_1\})$ into this equation, and you'll find $P(\{a_1\}) = \frac{1}{3}$.