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The formula for probability is

$\begin{array}{l}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{P}\mathbf{=}\frac{\mathrm{Favourable}\mathrm{out}\mathrm{comes}}{\mathrm{Total}\mathrm{Out}\mathrm{comes}}\\ \mathbf{P}\mathbf{(}{\mathbf{A}}^C\mathbf{)}\mathbf{=}\mathbf{1}鈭�\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\end{array}$

Here P(A)=0.05

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\mathbf{=}\mathbf{1}鈭�\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}鈭�\mathbf{0}\mathbf{.}\mathbf{05}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{95}\end{array}$

The sample spaces are:

(A, A, A, A), (N,N,N,N) ,(N,A,N,A) ,(A,N,A,N) ,(N,A,A,N), (A,N,A,A) ,(A,A,N,A) ,(A,A,A,N), (N,N,A,A), (A,A,N,N), (N,A,A,N), (A,N,N,A),(N,N,,N,A), (A,N,N,N) ,(N,A,N,N), (N,N,A,N).

MOW,

$\begin{array}{l}\mathbf{P}\mathbf{(}\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{)}\mathbf{=}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\\ \mathbf{=}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{95}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{95}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{95}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{95}\mathbf{)}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{00000625}\end{array}$

So, the probability is 0.00000625.

$\begin{array}{l}\mathbf{P}\mathbf{(}\mathbf{exectly}\mathbf{}\mathbf{two}\mathbf{)}\mathbf{=}\mathbf{(}\mathbf{N}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{A}\mathbf{)}\mathbf{+}(\mathbf{A}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{N})\mathbf{+}(\mathbf{N}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{N})\mathbf{+}(\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{A})\mathbf{+}(\mathbf{A}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{N})\mathbf{+}(\mathbf{A}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{A})\\ =6脳P(N,A,N,A)\\ \mathbf{=}\mathbf{6}\mathbf{脳}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\\ \mathbf{=}\mathbf{6}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{95}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{95}\mathbf{)}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0135}\end{array}$

Accordingly, the probability is 0.0135.

$\begin{array}{l}\mathbf{P}\mathbf{(}\mathbf{1}\mathbf{watch}\mathbf{}\mathbf{accurate}\mathbf{)}\mathbf{=}(\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{A})\mathbf{+}(\mathbf{A}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{N})\mathbf{+}(\mathbf{N}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{N})\mathbf{+}(\mathbf{N}\mathbf{,}\mathbf{N}\mathbf{,}\mathbf{A}\mathbf{,}\mathbf{N})\\ =4脳P(N,N,N,A)\\ \mathbf{=}\mathbf{4}\mathbf{脳}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{N}\mathbf{\right)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{4}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{\left)}\mathbf{\right(}\mathbf{0}\mathbf{.}\mathbf{95}\mathbf{)}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{000475}\end{array}$

The conclusion is that the probability is 0.000475, which is so low. as a result, there is skepticism, as the manufacturer said.

The probability of no accurate watches is 0.00000625, which is so low. Therefore, the manufacturers鈥� claim is not wrong.