To calculate the probability of having exactly 3 sunny days in the next 7 days, we use the Binomial Distribution formula:
P(X=k)=(kn)pk(1−p)n−k
Where:
- n = 7 (number of days)
- k = 3 (number of sunny days)
- p = 0.9 (probability of sunny day)
P(3)=(37)×0.93×(1−0.9)7−3
P(3)=3!(7−3)!7!×0.93×0.14
P(3)=3×2×17×6×5×0.729×0.0001
P(3)=35×0.729×0.0001=0.00255
This is a binomial probability problem where we're looking for exactly 3 successes (sunny days) in 7 independent trials (days), with each trial having a 90% probability of success.