What Is the Probability of Drawing a 2, 3, or 4 as the 13th Card?

[jackbauer]

Hi ppl, was hoping someone could point me in the right direction with this problem. 12 cards are dealt from a standard 52 pack of playing cards, 6 are kept face down, the others are 2 kings, two 3s, a 7 and a jack. Calculate the probability the 13th card drawn is a 2,3 or a 4.
Could someone please give me some help on how to proceed, thx
Jack

 

[mathman]

You have 6 known cards including 2 3's. There are 46 unknown cards including 4 2's 2 3's and 4 4's, a total of 10 desired cards. Therefore the probability that the next card chosen is one of these is 10/46. The 6 previously chosen, but unknown, cards are irrelevant.

 

[Architeuthis Dux]

ie

The probability of drawing a 2, 3, or 4 as the 13th card in a deck of playing cards can be calculated by dividing the number of desired outcomes (drawing a 2, 3, or 4) by the total number of possible outcomes (drawing any card from a deck of 52 playing cards).

In this case, we have already been given information about the first 12 cards that were dealt. Out of those 12, we know that there are 2 kings, 2 3s, a 7, and a jack. This leaves us with 6 unknown cards.

To calculate the probability of drawing a 2, 3, or 4 as the 13th card, we first need to determine the total number of possible outcomes for the 13th card. Since we are dealing with a standard deck of 52 playing cards, there are 52 possible outcomes for the 13th card.

Next, we need to determine the number of desired outcomes. Since we want to draw a 2, 3, or 4, we need to calculate the number of remaining cards in the deck that fit this criteria. There are 4 2s, 4 3s, and 4 4s in a standard deck, so there are 12 desired outcomes.

Now, we can plug these numbers into the formula for probability:

Probability = Desired outcomes / Total outcomes

Probability = 12/52 = 3/13

Therefore, the probability of drawing a 2, 3, or 4 as the 13th card is 3/13 or approximately 0.23.

I hope this helps and points you in the right direction to solve the problem. Remember to always carefully consider the given information and use the appropriate formula to calculate probability.