Weather records show that the probability of rainfall in florida in june is 0.86. what is the probability that it rains there in june at least 9 times in a decade?

R - it is rain  (probablity: 0.86)
N - it is not rain (probablity: 1-0.86 = 0.14)
You've got these cases:

R R R R R R R R R N
R R R R R R R R N R
R R R R R R R N R R 
. . . 
N R R R R R R R R R     -  it is 10 cases.  Probablity each case is
(0.86)^9 * 0.14 - it is approximately  0.036   (9R and 1N - you multiply everything)

It is 10 cases so you have to multiply by 10  and you get 0.36

There is also eleventh case:

R R R R R R R R R R 

Probablity is (0.86)^10 approximately 0.22

Add these cases and you'll get your probablity:  0.36 + 0.22 = 0.58 

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