$1.$ A binary bit is transmitted with redundancy. Instead of sending a binary $1,$ three binary $1$s will besent. The receiver will decode the received signal by majority rule. In every three bits, if thereare two zeros, and one binary $1,$ or all three are zeros, the information bit will be decoded as abinary $0.$ If there are two ones and one binary zero, or all three ones, the information bit will bedecoded as a binary $1.$ If the probability in transmitting a bit without any error is $0\mathrm{.}4,$ what is theprobability the receiver will be able to decode the correct information data bit?