Question

The following table gives the total endothermic reactions involving sodium bicarbonate

Final Temperature Conditions	Number of Reactions
266 K	10
271 K	60
274 K	92

Assume that reactions are independent. What is the probability that the 2^nd reaction to result in a final temperature less than 272K occurs within three or fewer reactions? Report answer 3 decimal places.

Answer 1

P( final temperature less than 272K )=(10+60)/(10+60+92)=0.4321

here this follows negative binomial distribution with parameter r =2 and p=0.4321

probability that the 2^nd reaction to result in a final temperature less than 272K occurs within three or fewer reactions :

P(X<=3)=1-P(X>=4)=

1-∑a=0r-1     (xCa)pa(1−p)(x-a)    =

0.399