The probability that more than 7 patients will have this mild side effect is ___. (Round to three decimal places as needed.)
Answer:
Given:
Probability of success $(p)=0.25$
Sample size $(n)=16$
Solution:
The probability that more than 7 patients will have this mild side effect:
$$ \text{P}(x > 7) = \sum_{8}^{16} \binom{n}{x} \cdot p^x \cdot (1-p)^{n-x} $$ $$ = \sum_{8}^{16} \binom{16}{x} \cdot 0.25^x \cdot (1-0.25)^{16-x} $$ $$ = 0.0271 $$
Final Answer:
The probability that more than 7 patients will have this mild side effect $=0.0271 $
