Question

there were ten red battles sitting on the wall. the probability of a red bottle accidentally falling is 0.95.what is the probability that fewer than 8 of the green bottle accidentally fall

Answer 1

Solution:

If accidentally falling probability of a red bottle from 10 bottles $P(1/10)=0.95;$ then accidentally falling probability of one red bottle independently:

$P_1=\frac{P(1/10)}{10}=0.095;$ So, we will use Bernoulli's formula for probability, because independently falling probability of bottles (red and green) the same. So, in our case we need to find probability fewer than 8 of green bottles. It means $m_i=0, 1,2,3,4,5,6\space and\space7;$ $n=8;$

$P=\displaystyle\sum_{i=0}^{n-1}\frac{n!}{(n-m_i)!m_i!}(P_1)^{m_i}(1-P_1)^{8-m_i}=\displaystyle\sum_{i=0}^{7}\frac{8!}{(8-m_i)!m_i!}(0.095)^{m_i}(0.905)^{8-m_i}=0.9999;$

I used Excel for calculation.

Answer:

$P=99.99\%.$