If on the average the rain falls on twelve days in every thirty days, find the probability the first three days of a given week will be fine and remaining wet.

1. If on the average the rain falls on twelve days in every thirty days,
find the probability the first three days of a given week will be fine
and remaining wet.
Solution:
𝑛 = 7
Probability that rain is not falls is
𝑃 =
18
30
= 0.6
and 𝑞 =
12
30
= 0.4
𝑷(𝐟𝐢𝐫𝐬𝐭 𝐭𝐡𝐫𝐞𝐞 𝐝𝐚𝐲𝐬 𝐨𝐟 𝐚 𝐠𝐢𝐯𝐞𝐧 𝐰𝐞𝐞𝐤 𝐰𝐢𝐥𝐥 𝐛𝐞 𝐟𝐢𝐧𝐞 𝐚𝐧𝐝 𝐫𝐞𝐦𝐚𝐢𝐧𝐢𝐧𝐠 𝐰𝐞𝐭) = 𝒑𝒙
𝒒𝒏−𝒙
𝑷(𝐟𝐢𝐫𝐬𝐭 𝐭𝐡𝐫𝐞𝐞 𝐝𝐚𝐲𝐬 𝐨𝐟 𝐚 𝐠𝐢𝐯𝐞𝐧 𝐰𝐞𝐞𝐤 𝐰𝐢𝐥𝐥 𝐛𝐞 𝐟𝐢𝐧𝐞 𝐚𝐧𝐝 𝐫𝐞𝐦𝐚𝐢𝐧𝐢𝐧𝐠 𝐰𝐞𝐭) = (𝟎. 𝟔)𝟑(𝟎. 𝟒)𝟕−𝟑
𝑷(𝐟𝐢𝐫𝐬𝐭 𝐭𝐡𝐫𝐞𝐞 𝐝𝐚𝐲𝐬 𝐨𝐟 𝐚 𝐠𝐢𝐯𝐞𝐧 𝐰𝐞𝐞𝐤 𝐰𝐢𝐥𝐥 𝐛𝐞 𝐟𝐢𝐧𝐞 𝐚𝐧𝐝 𝐫𝐞𝐦𝐚𝐢𝐧𝐢𝐧𝐠 𝐰𝐞𝐭) = (𝟎. 𝟔)𝟑(𝟎. 𝟒)𝟒
𝑷(𝐟𝐢𝐫𝐬𝐭 𝐭𝐡𝐫𝐞𝐞 𝐝𝐚𝐲𝐬 𝐨𝐟 𝐚 𝐠𝐢𝐯𝐞𝐧 𝐰𝐞𝐞𝐤 𝐰𝐢𝐥𝐥 𝐛𝐞 𝐟𝐢𝐧𝐞 𝐚𝐧𝐝 𝐫𝐞𝐦𝐚𝐢𝐧𝐢𝐧𝐠 𝐰𝐞𝐭) = 𝟎. 𝟎𝟎𝟓𝟓