# 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.

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.