There is a game with three types of cards.

Win cards, If you get one of these, you win.

Lose card, if you get this, you lose.

Revive card: If you get one of these, you draw another card.

Now Initially we have a deck of cards of all three types. p Win cards, q Lose cards, and r revive cards. The deck is well shuffled.

Then we take the first s cards of the deck ( s < p + q ) and discard them. What is the probability That I would win the game now.

This is an excercise from my book. How do we approach this problem?

  • $\begingroup$ "This is an excercise from my book", really, I thought you got tricked trying to solve codechef.com/JULY13/problems/PROB @admin, bring this post down, its a question from live contest. $\endgroup$ – AdhogCrusher Jul 8 '13 at 21:34

The probability that the first win card comes before the first lose card is unchanged at $\dfrac{p}{p+q}$.

If that is not clear, imagine taking the discarded cards and putting them at the bottom of the deck,


Let $P(W)$ be the probability of winning and let $P_i(L)$ be the probability of drawing a lose card at the $i$th trial and let $P_j(R)$ be the probability of drawing a revive card at the $j$th trial. Then

$P(W) = 1 - \sum_{i=1}^N P_i (L)\prod_{j=1}^{i-1} P_j(R)$

where $N=r+1$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.