probability - Difference between two statements I have the following scenario.
There are a number of people on an island. Each person has a chance of 0.015 of dying on any given day, independent of other people on the island. 
I have two different probabilities for two statements that were calculated by the professor, but I can't see the difference between the meaning of the two statements.
Statement 1: Person A survived the sixth day.
Probability of statement 1: 
$P=(1-0.015)^5\cdot 0.015=0.0139$ (probability person A died on the 6-th day)
$P(Statement 1)=1-0.0139=0.986$
Statement 2: Person A survived for 6 straight days.
Probability of statement 2:
$P(Statement 2)=0.985^6=0.913$
I understand how each probability was calculated, but I don't see the difference between each statement logically. Please explain what is the difference, or give an example when statement 1 occurs but statement 2 doesn't, or vice versa.
Thank you.

There is nothing in the model that prevents a person of dying on day one and then living on day two. This is why the two statements are different:


*

*Statement 1 is the negation of "the person did not die on days 1 through 5 and died on day 6"

*Statement 2 means "the person did not die on days 1 through 6"


Let $D_i$ be the event of the person dying on day $i$, then
$$ \text{Statement 1} = \neg\big((\neg D_1)(\neg D_2)(\neg D_3)(\neg D_4)(\neg D_5) D_6\big) = $$
by De Morgan
$$  =  D_1 \vee D_2 \vee D_3 \vee D_4\vee D_5\vee \neg D_6$$
which is true when the person dies on any one of the days 1 through 5.
