Three cards are drawn from an ordinary 52 deck of cards without replacement (drawn cards are not placed back in to the deck). Find the probability that the 3 cards are non – heart, heart (in the order)
Find the probability that the 3 cards are non – heart, heart (in the order)
so, what's the 3rd card?
To find the probability that the three drawn cards are non-heart, heart (in that order), we need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of non-heart cards in the deck.
In a standard deck of 52 playing cards, there are 13 hearts. Therefore, the number of non-heart cards is 52 - 13 = 39.
Step 2: Determine the number of hearts in the deck.
Since three cards are drawn without replacement, after the first card is selected, there are 51 cards left in the deck. So, the number of hearts in the deck is 13.
Step 3: Calculate the probability.
The probability of drawing a non-heart card first is 39/52 (since there are 39 non-heart cards out of 52 total cards).
After drawing a non-heart card, there will be 51 cards left in the deck, with 13 of them being hearts.
The probability of drawing a heart second is 13/51.
Finally, the probability of the third card being non-heart is also 39/50 because, after the second card is drawn, there will be 50 cards left in the deck, with 39 non-heart cards.
To find the probability of the three cards being non-heart, heart (in order), we multiply these probabilities together:
Probability = (39/52) * (13/51) * (39/50)
Simplifying this expression gives us the answer.