What is the Probability of Getting a Jack from a 52-Card Deck on Both the First and Second Draw if the Cards are not Replaced?

Question: What is the probability of getting a jack from a 52-card deck on both the first and second draw if the cards are not replaced?

1. 1/13
2. 1/17
3. 30/221
4. 7/221
5. 1/221

“What is the probability of getting a jack from a 52-card deck on both the first and second draw if the cards are not replaced?” - is the topic of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Prep Plus 2021”. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements.GMAT data sufficiency comprise 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

As there are 4 jacks in a pack of 52-card deck

So, Probability = Number of favorable outcomes/Total outcomes

Firstly, we will find the probability of getting a jack in first draw

Formula to calculate this is:

Probability = Number of favorable outcomes in first draw/Total outcomes

Probability = 4C1 / 52C1

Now, we will check the probability of getting a jack on second draw.

Formula to calculate this is:

Probability = Number of favorable outcomes in second draw/Total outcomes

Number of favorable outcomes = 3C1 (As we already drew one card)

Hence, Required Probability = 3C1 / 51C1

Now, multiply both the probabilities, we will get:

So, 4*3 /52*51 = 1/221

Correct option: E

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