A game is played with a standard deck of cards. Each face card has a value of 10, each ace has a value of 1 and each number card is equal to its number, Two cards are drawn without replacement. If one is the queen of hearts what is the probability that the sum is greater than 18?

Question

kropot72 · Answer

The aces and all number cards with numbers 2 to 8 inclusive, totalling 32 cards, cannot give the required result. This leaves 18 cards that can give a sum greater than 18. There are 50 cards remaining. the probabilty of Sum > 18 is:
$$\frac{18}{50}$$

anonymous · Answer

how did you get 18?

kropot72 · Answer

Assuming the queen of hearts is drawn first there will be 19 cards remaining that can give the required result and a total of 51 cards left in the pack. In this case:$$P(s>18)=\frac{19}{51}$$

anonymous · Answer

An 8 wouldn't give you a sum of greater than 18, but a 9 would. There are 4 of those. Same with a 10, jack, queen, or king. Except since 1 queen has already been drawn, there are only 3 more that could be drawn.