The probability that, among ten of these people, at least 3 have brown eyes is ___. (Round to three decimal places as needed.)
Answer:
Given:
Probability of success $(p)=0.52$
Sample size $(n)=10$
Solution:
The probability that among ten of these people at least 3 have brown eyes:
$$ \text{P}(x \geq 3) = \sum_{3}^{10} \binom{n}{x} \cdot p^x \cdot (1-p)^{n-x} $$ $$ = \sum_{3}^{10} \binom{10}{x} \cdot 0.52^x \cdot (1-0.52)^{10-x} $$ $$ = 0.9580$$
Final Answer:
The probability that among ten of these people at least 3 have brown eyes $=0.9580$
