Probability of drawing in a deck of cards

Question

Cesia_Haven13Tyro

Asked: April 18, 20212021-04-18T07:40:15+00:00 2021-04-18T07:40:15+00:00In: High School/Senior Secondary School, Statistics and Probability

What is the probability of drawing

an ace and king in a deck of cards?

You must login to add an answer.

Need An Account,

acedstud · Accepted Answer · 2021-04-18T10:54:07+00:00

When two cards are picked from a deck of cards, there are two cases, namely, with replacement and without replacement.

Case 1: With replacement

There are 4 aces, 4 kings, and a total of 52 cards in a standard deck of card.

The probability of picking an ace is $\dfrac{4}{52}=\dfrac{1}{13}$ and the probability of picking a king is $\dfrac{4}{52}=\dfrac{1}{13}$ .

Thus, the probability of picking an ace AND a king is $\dfrac{1}{13}\times\dfrac{1}{13}=\dfrac{1}{169}$ .

Case 1: Without replacement

There are 4 aces, 4 kings, and a total of 52 cards for the first pick and a total of 51 cards for the second pick in a standard deck of card.

The probability of picking an ace first is $\dfrac{4}{52}=\dfrac{1}{13}$ and the probability of picking a king next is $\dfrac{4}{51}$ .

Thus, the probability of picking an ace AND a king is $\dfrac{1}{13}\times\dfrac{4}{51}=\dfrac{4}{663}$ .

AcedStudy Latest Questions