$3.$ In a binary communication channel the probability of receiving a $\text{'}1\text{'}$ f a transmitted $\text{'}1\text{'}$ is $0\mathrm{.}90$ and the probability of receiving a $\text{'}0\text{'}$ from a mitted $\text{'}0\text{'}$ is $0\mathrm{.}95.$ If the probability of transmitting a $\text{'}1\text{'}$ is $0\mathrm{.}60$ then tra obta the probability that I, $\backslash$mathcal$\{$E$\}($I$)\text{'}$ is received and $[,$ mathcal R $($I$)\text{'}$ is received from a tran mitted $\text{'}1\text{'}.$