Respuesta :
The problem can be solved using the Binomial Probability Formula:
[tex]P(X)=(^n_X)\cdot p^X\cdot(1-p)^{n-X}[/tex]where X is the number of successes, n is the number of times an event can occur, and p is the probability of success.
From the question, we can get the following parameters:
[tex]\begin{gathered} n=12 \\ p=87\%=0.87 \end{gathered}[/tex]We can have that:
[tex]P(X\ge10)=P(10)+P(11)+P(12)[/tex]We have that:
[tex]\begin{gathered} X=10 \\ P(10)=(^{12}_{10})\cdot0.87^{10}\cdot(1-0.87)^{12-10} \\ P(10)=\frac{12!}{10!(12-10)!}\cdot0.87^{10}\cdot(1-0.87)^{12-10} \\ P\mleft(10\mright)=0.2771 \end{gathered}[/tex]Using the steps above, we can calculate the other values to be:
[tex]\begin{gathered} P(11)=0.3372 \\ P(12)=0.1880 \end{gathered}[/tex]Therefore, the probability is calculated to be:
[tex]\begin{gathered} P(X\ge10)=0.2771+0.3372+0.1880 \\ P(X\ge10)=0.8023 \end{gathered}[/tex]The probability is about 0.8023.
