During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0…
During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6 . The probability that in a given week there will be exactly two days with severe fog is
$\frac{6048}{5^7}$
$\frac{2016}{5^7}$
$\frac{3024}{5^7}$
$\frac{12096}{5^7}$
Solution
$P($ severe fog on a day $)=0.6$.
$\therefore P($ no severe fog on a day $)=0.4$
Total number of days $=7$,
$\therefore P$ (exactly 2 days of sever fog)
$
\begin{aligned}
& ={ }^7 C_2 \times(0.6)^2(0.4)^5 \\
& =\frac{21 \times 9 \times 32}{5^7}=\frac{6048}{5^7}
\end{aligned}
$