Answer
a) .0001
b) $P(-1)=.9999$; $P(4,999)=.0001$
c) .0365
d) .0352
e) -.5 dollars
Work Step by Step
a) Your probability is:
$\frac{1}{10^4}=.0001$
b) Using the value above, we find that the probability of losing a dollar is: $P(-1)=.9999$. Thus, the probability of winning 4,999 dollars is: $P(4,999)=.0001$.
c) We multiply the probability by 365:
$.0001 \times 365=.0365$
d) The probability of winning exactly once is equal to the probability of winning once minus the probability of winning a second time in the 365 days:
$=.0365-.0365^2=.0352$
e) Every 10,000 times, you win 5,000 dollars, but it costs you 10,000 dollars to buy the tickets. Thus, the expected value is:
$= \frac{5,000-10,000}{10,000}=-.5$
