Answer to Question #304220 in Statistics and Probability for Sam

Question

A deck of 52 playing cards has 4 aces. The probability of getting one ace less than zero

Answer 1

The number of aces in a pack of 52 card is 4, so the probability that the card drawn is an ace is,

P=4/52

Now, since one card is been chosen, then the total number of aces left is 3 and the total number of cards left is 52−1=51.

The probability that the card drawn is an ace is,

P=3/51

As two cards are been chosen, then the total number of aces left is 2 and the total number of cards left is 51−1=50.

The probability that the card drawn is an ace is,

P=2/50

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Again, since three cards are been chosen, then the total number of aces left is 1 and the total number of cards left is 50−1=49.

The probability that the card drawn is an ace is,

P=1/49

By multiplication law of probability, we have

p= ( (4/52) * (3/51) * (2/50) * (1/49) )

Therefore the required probability equals 1/270725