A lottery game, Big Four, is played by choosing four numbers from 1 to 15 (no repetition of numbers; order of the numbers does not matter). You win the top prize in a particular draw if the four numbers on your ticket are the winning numbers. There is only one top prize in each draw.
You have decided to have the following four numbers: 2 – 7 – 11 – 15 and buy only one lottery ticket of this number combination in each draw for the next 200 draws.
What is the likelihood for you to win the top prizes in the next 200 draws?
My Answer (Or thinking flow)
So we consider the chance of me winning at any draw. It is $\frac{1}{15}^4=\frac{1}{50625}$.
I can win in many different scenarios. Win all 200 draws, win no draws, win the 6th draw etc. Gotta consider all scenarios.
- 0 wins. Likelihood $=0$
- 1 win. I can win in any of the 200 draws. Likelihood $\frac{1}{50625}*^{200} P_{1}=\frac{1}{50625}*200=\frac{8}{2025}$
- 2 wins. I can win in any two of the 200 draws. Likelihood $\frac{1}{50625}*^{200} P_{2}=\frac{1}{50625}*39800=\frac{1592}{2025}$
- Continuing.....................Till 200
I believe my answer to be very wrong, as I am supossed to do it with a faster method. My tutor is known for giving not-so straightforward questions, so I'm wondering if I need to consider another way, or I could be wrong. Any alternatives welcome too!