Probability?

1)
Prob (rain on 0 day in 2 weeks) = (0.7669)^14
Prob (rain on 1 day in 2 weeks) = 14 × 0.2331 × (0.7669)^13
Prob (rain on 2 days in 2 weeks)
= C(14,2) × (0.2331)² × (0.7669)^12 = 91 × (0.2331)² × (0.7669)^12
Prob (rain on 3 days in 2 weeks)
= C(14,3) × (0.2331)³ × (0.7669)^11
= 364 × (0.2331)³ × (0.7669)^11

∴ Prob (rain on at least 4 days in 2 weeks)
= 1- (0.7669)^14 - 14 ×0.2331 ×(0.7669)^13 - 91×(0.2331)² × (0.7669)^12
- 364×(0.2331)³ × (0.7669)^11
= 1- (0.7669)^11 [(0.7669)³ +14×0.2331 × (0.7669)² +91×(0.2331)² × (0.7669)
+ 364×(0.2331)³ ]
= 0.4186

2)
Prob (rain on 1st,2nd in first half of Nov) = (0.2331)² × (0.7669)^13

Event (rain on exactly 2 consecutive days in first half on Nov) , E
= {(1,2),(2,3),(3,4), ..., (14,15)}
i.e. n(E) = 14

∴ Prob (rain on exactly 2 consecutive days in first half on Nov)
= 14 ×(0.2331)² ×(0.7669)^13
= 0.02414 ( to 4 sig. fig.)