Suppose that you hold one of the 100 tickets in a lottery. There are 5 prizes altogether, 1st prize for the first draw, 2nd prize for the second draw, etc. Assume the draws are without replacement. Find the probability that you win one prize.
My attempt:
1/100+1/99+1/98+1/97+1/96.
Not sure if this is correct. Please help
Edit: or would it be $\dfrac{5 \choose 1}{100 \choose 5}$?
Best Answer
Since you hold one ticket, the five prizes must be chosen from the other tickets. Thus the probability that you do not win any prize is $\dfrac{\binom{99}{5}}{\binom{100}{5}}$ and the probability that you win one prize is $1 - \dfrac{\binom{99}{5}}{\binom{100}{5}}$