You draw a card from a deck and it is an ace. Without replacing the card, you draw a second card.
Answers
Answer:
Step-by-step explanation:
First of all, we must establish a set of facts, pre-conditions if you like.
Your question refers to a standard deck of 52 cards.
Said deck of cards is shuffled and does not contain any markings that may assist you when drawing a card.
After successfully drawing your Ace and placing it back in the deck, the cards are reshuffled. As knowing the location of the previous Ace and subsequently not picking it increases your chances, albeit it very slightly, of drawing a face card.
Now that we’ve established these facts, we can calculate the probability. As the draws are independent of each other, the probability of drawing one of four Aces from a deck = 4/52
, while the probability of drawing one of twelve Face cards from a deck = 12/52
. These probabilities will not change.
To calculate the probability of both events happening, providing that the card is replaced and pre-condition 3 is met, we multiply the fractions, giving us 48/2704
.
Therefore, the probability of drawing an Ace from a standard deck of cards, replacing it then drawing any Face card is:
P=
4/52∗12/52
=
48/2704
=
3/169
=
0.017751…