A die is weighted so that the probability of its landing face i uppermost is i/21. This die is thrown and if i shows uppermost, i fair dice are thrown
(i = 1,2,3,4,5,6). A total score is obtained by summing the numbers showing uppermost on these fair dice.
1) Find the probability that the total score is 4
2) Find the probability that 2 fair dice were thrown, given that the total score is 4.
At the first attempt of this question, I got there are 4 ways which you can a total score of 4 when you roll i dice.
When throwing: 1 die gives only one choice, that is number 4
2 dice give (1,3),(2,2),(3,1) which the sum is 4
3 dice give (1,1,2),(1,2,1),(2,1,1) which the sum is 4
4 dice give (1,1,1,1)
Cuz I am not allowed to use tree diagram, so I have to use the formulae of probability
I've just done up to here then I got stuck, I think somehow we have to use the law of total probability.
Can some body help me to do part 1 and give hints on part 2 please?
Thank you very very much for your time.