When sent a questionnaire, the probability is $0\mathrm{.}5$ that any particular individual to whom it is sent will respond immediately to that questionnaire. For an individual who did not respond immediately, there is a probability of $0\mathrm{.}4$ that the individual will respond when sent a follow$-$up letter. If the questionnaire is sent to $4$ persons and a follow$-$up letter is sent to any of the $4$ who do not respond immediately, what is the probability that at least $3$ never respond?