Answer: 0.3125
Step-by-step explanation:
Given : The probability of rain on any given day in Chicago (independent of what happens on any other day) during the summer is 50% =0.5
Number of days from July 4 through July 8, inclusive = 5
According to the Binomial distribution for any random variable X , the probability of getting x successes in n trials :
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
, where p is the probability of getting success in each trial.
Let x = number of rainy days .
As per given , we have n= 5 , p=0.5
Then, the probability of having exactly 3 rainy days from July 4 through July 8, inclusive will be [tex]P(X=3)=^5C_3(0.5)^3(1-0.5)^{5-3}[/tex]
[tex]=\dfrac{5!}{3!(5-3)!}(0.5)^5\\\\=\dfrac{5\times4\times3!}{3!(2)!}(0.03125)=10(0.03125)=0.3125[/tex]
Hence, the probability of having exactly 3 rainy days from July 4 through July 8, inclusive= 0.3125
