Suppose you draw two cards from a 52-card deck. Compute the following probabilit

Question

Suppose you draw two cards from a 52-card deck. Compute the following probabilities. Give your answers to four decimal places.

What is the probability that both cards are aces if you replace the first card before drawing the second?

What is the probability that both cards are aces if you do not replace that first card before drawing the second?

What is the probability that the first card is an ace and the second is a king if you replace the first card before drawing the second?

What is the probability that the first card is an ace and the second is a king if you do not replace the first card before drawing the second?

What is the probability that both cards are the same suit if you replace the first card before drawing the second?

What is the probability that both cards are the same suit if you do not replace the first card before drawing the second?

Explanation / Answer

In case of with replacement we have the same number of cards again to select however in case of without replacement the number of cards available to select changes.

#1.
P(both aces with replacement) = 4/52 * 4/52 = 0.00592

#2.
P(both aces without replacement) = 4/52 * 3/51 = 0.0045

#3.
P(first ace second king with replacement) = 4/52 * 4/52 = 0.00592

#4.
P(first ace second king without replacement) = 4/52 * 4/51 = 0.0060

#5.
P(same suit with replacement) = 4C1 * 13/52 * 13/52 = 1/4 = 0.25

#6.
P(same suit without replacement) = 4C1 * 13/52 * 12/51 = 12/51 = 0.2353

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