# Question #bb618

##### 1 Answer

a)

b)

c)

#### Explanation:

Probability of winning the first game means he must win the first and the outcome of winning or losing beyond that is not meaningful so let's think about possible outcomes

#w1 =# win or lose#w2 =# win or lose#w3 =# win or lose

so in the case that w1=win then w2 and w3 can be a win or lose. This means that the total outcomes is

let's just say

another outcome is

continuing this line of thinking the other two outcomes where w1 wins is thus

and

now if we want to determine winning the first game we can consider the 4 outcomes or

a) =

you notice this is the same result for probability of winning a game. This makes sense because if we were to construct a tree you would see that winning the first game is always

the probability of winning the game exactly once is the same as

b =

the probability of winning 2 out of 3 games the same as

c =

it might not seem intuitive that we include the scenario where we win in all 3 games but this is because this is a valid outcome for winning 2 out of 3 times and the question is not exactly 2 out of 3 times