Question

A game where a player randomly pulls one prize from a pool of several different prizes. Moreover, the prize pool is not replenished after each pull. A person is playing a gacha game where the prize he wants is one of ten available prizes in the pool. What is the probability that he gets the prize he wants exactly on his third pull?

Answer 1

Need to find P(gets the specific prize on the third pool)

Now Total prizes = 10,

Let us denote drawing the specific prize as a win and any other as loss)

Hence we need to P(win on third draw)

P(win on third draw) = P(loss on first draw) * P(loss on second draw | loss on first draw) * P(win on third draw | loss on second draw)

P(loss on first draw) = 9/10 -- choose anything other than specific prize out of 10 prizes

P(loss on second draw | loss on first draw) = 8/9 -- Choose anything other than specifc prize out of remaining 9 prizes after first draw

P(win on third draw | loss on second draw) = 1/8 -- Choose specific prize out of remaining 8 prizes

P(gets the specific prize on the third pool) = 9/10*8/9*1/8 = 1/10

Ans 1/10