Question

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?
0.26
0.41
0.22
0.58

Answer 1

@taylorannbs @kohai

Answer 2

During any one year, the probability of rainfall is 0.86; call this your success probability. The probability of failure (no rain) is then 1-0.86 = 0.14.

This is a binomial probability, meaning for \(n\) observations, the probability that success occurs at least \(k\) times is equivalent to
\[\large P(X\ge k)=\sum_{x=k}^n \binom nx p^x(1-p)^{n-x}\]
Translated to this context, you want
\[\large\begin{align*}P(X\ge9)&=\sum_{x=9}^{10}\binom{10}x(0.86)^x(0.14)^{10-x}\\
&=\binom{10}9(0.86)^9(0.14)^{10-9}+\binom{10}{10}(0.86)^{10}(0.14)^{10-10}\\
&=10(0.86)^9(0.14)+(0.86)^{10}\\
&\approx0.22
\end{align*}\]

Answer 3

0.22 is wrong i got it wrong.

Answer 4

0.41 is wrong also

Answer 5

It's D 0.58