Consider a standard deck of 52 cards (13

lolgirl1213

lolgirl1213

Answered question

2022-05-02

Consider a standard deck of 52 cards (13 cards each in 4 suits, clubs, spades, diamonds and hearts).  What is the probability of picking out a jack of spades and then, without replacing the card to the deck, pick out a jack of diamonds?

 

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-04Added 184 answers

Let's first find the probability of picking out a jack of spades from a standard deck of 52 cards. The probability of picking out a jack of spades is given by:
P(Jack of spades)=Number of Jack of spadesTotal number of cards=152
Since we do not replace the card back to the deck, the total number of cards left in the deck will be 51. The number of Jack of diamonds left in the deck will be 1. Therefore, the probability of picking out a jack of diamonds after picking out a jack of spades is given by:
P(Jack of diamonds after Jack of spades)=Number of Jack of diamondsTotal number of cards after Jack of spades=151
Now, we can find the probability of picking out a jack of spades and then, without replacing the card to the deck, pick out a jack of diamonds by multiplying the probabilities of the two events:
P(Jack of spades and Jack of diamonds)=P(Jack of spades)·P(Jack of diamonds after Jack of spades)
P(Jack of spades and Jack of diamonds)=152·151
P(Jack of spades and Jack of diamonds)=12652

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