Hey sorry I need help in ii

In the Jackpot Lottery, the probability of the Jackpot prize being won in any draw is approximately 1 in 50.

i) What is the probability that the jackpot prize will be won in each of the three consecutive draws?

ii) How many consecutive draws must be made for it to be 99% certain that a Jackpot prize will have been won?

Basically see above for the answer. Just want to provide a small remark for extra intuition.

The question is probably doable directly, but it would probably be messy. Because you only require the probability that it is won

**at least** one out of the first \(n\) draws, you get different results depending on if it's won exactly once, twice, three times, all the way up to \(n\) times.

And in 2U maths, of course we learn that the complement is a natural way to navigate around the "at least" issue wherever possible. The complement is when you don't win it

**at all**, which you know can only happen one possible way. (Namely, it is never won.)

So this probability will be \( \left( \frac{49}{50} \right)^n \), and hence what we require is \( 1 - \left( \frac{49}{50} \right)^n = 0.99 \). Which of course, becomes what was computed above.

-snip-

You can use \times for \(\times\) and you should use \ln for \(\ln\) for better LaTeX in the future