Probability and Cards

What is the probability of picking up an ace in a 52 card deck? The probability of picking up an ace in a 52 deck of cards is 4/52 since there are 4 aces in the deck. The odds of picking up any other card is therefore 52/52-4/52=48/52. What is the probability of picking up an ace or king in a 52 card deck? The probability of picking up an ace or a king is 8/52 since in a deck of 52 cards there are 4 aces and 4 kings, which totals 8. The probability of not picking up an ace or king is simply 52/52-8/52=44/52.

Now let's make things more complicated. What is the probability of picking an ace in five consecutive attempts in a 52 card deck? In order to determine this probability, first you must determine the probability of not picking up an ace in 5 attempts ; removing a non-ace after each attempt. The probability of not picking up an ace in the first attempt is 48/52. The probability of not picking an ace in the second attempt is 47/51. This is the case because you had previously removed one of the non-aces in the first attempt reducing the non-aces from 48 to 47. Also, the total amount of cards also dropped after the first attempt reducing the total number of cards from 52 to 51. Continuing with this logic on the third attempt the probability of picking a non-ace is 46/50. You can see that the numerator and denominator are both being reduced by 1 with each attempt. On the fourth attempt the probability of picking a non-ace is 45/49 and on the fifth attempt is 44/48. So, the total probability of picking a non-ace in 5 consecutive attempts removing the card after each attempt is the product of each individual attempt. The product of each individual attempt is 48/52*47/51*46/50*45/49*44/48=0.66. Multiplying this value by 100 gives you 66 percent. So there is a 66 percent chance of not picking up an ace in 5 consecutive attempts removing the card after each attempt.

Now in order to determine the probability of picking up an ace in 5 consecutive attempts you must subtract 66 from 100 which gives you 34 percent. So, there is a 34 percent chance of picking up an ace in 5 consecutive attempts removing the card after each attempt .

Playing cards involves probability. The better you understand probability, then the better you will play!