Question

Problem 4. Alice and Bob draw a number from {3, 4, 5}, with replacement, in turn. Alice starts first. If someone’s draw makes (for the first time) the total sum of all the numbers drawn so far at least 10, he/she wins and the game ends. What is probability that Alice loses?

I am not sure if this question requires the use of conditional probabiltiy.

Answer 1

here if by strategy Alice plays the game she will always wins ; cause if she draws 3 or 4 on first turn ; then Bob can draw anything from 3,4 or 5 which will not make up sum to 10 ; and on second turn Alice can have sum at least 10,

threfore by strategy  probability that Alice loses =0

However if number is drawn randomely:

probability that Alice loses =P(alice draw 3, Bob draws 3 and then Alice draw 3)+P(Alice draw 5 and Bob draws 5) =(1/3)*(1/3)*(1/3)+(1/3)*(1/3)=4/27

( please revert for any clarification required)