It has been shown that 30% of a certain group of people own a pet. Find the probability that, among nine of these people, at least 2 own a pet.

The probability that, among nine of these people, at least 2 own a pet is ___. (Round to three decimal places as needed.)


Answer:
Given:

Probability of success $(p)=0.30$

Sample size $(n)=9$

Solution:
The probability that among nine of these people at least 2 own a pet:
$$\text{P}(x\ge 2)=\sum _2^9(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1-p{)}^{n-x}$$ $$=\sum _2^9(\genfrac{}{}{0ex}{}{9}{x})\cdot {0.30}^x\cdot (1-0.30{)}^{9-x}$$ $$=0.804$$

Final Answer:
The probability that among nine of these people at least 2 own a pet $=0.804$