Answer: P(x) = (7/x) * 0.4 ^x * 0.6^(7-x)• We can design the simulation to predict the probability from the binomial disribution .
• P = 40 % /100 = 0.4
(1-P) = 60% /100 = 0.6
n = 7
[tex]\begin{gathered} P(x)\text{ = }\begin{bmatrix}{n} & {} \\ {x} & \end{bmatrix}P^x(1-P)^{n-x\text{ }} \\ \text{ =}\begin{bmatrix}{7} & {} \\ {x} & \end{bmatrix}P^x(1-P)^{(7-x)} \\ \text{ = }\begin{bmatrix}{7} & {} \\ {x} & {}\end{bmatrix}\cdot0.4^x\cdot0.6^{(7-x)} \end{gathered}[/tex]
This means that our probabilty of 40% chance of rain each day for 7 day a week is given by : P(x) = (7/x) * 0.4 ^x * 0.6^(7-x)
