# from a pack of 52 cards, two cards are drawn together at random. evaluate probability of both the cards being queen?

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## From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

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## From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

**A**

15 1

**B**

57 25

**C**

256 35

**D**

221 1 Easy Open in App Solution Verified by Toppr

Correct option is D)

Let S be the sample space.Then, n(S)= 52 C 2 = (2×1) (52×51) =1326.

Let E= event of getting 2 kings out of 4.

∴n(E)= 4 C 2 = 2×1) (4×3) =6. ∴P(E)= n(S) n(E) = 1326 6 = 221 1 .

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## From a pack of 52 cards, two cards are drawn toget

Probability Questions & Answers : From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

78 Q:

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

A) 1/15 B) 1/221 C) 25/57 D) 35/256 Answer: B) 1/221 Explanation:

Let S be the sample space

Then, n(S) = 52 C 2 52C2 = 1326.

Let E = event of getting 2 kings out of 4.

n(E) = 52*51 2*1 52*512*1 = 6. 4 C 2 4C2 => 4*3 2*1 4*32*1 P(E)= n(E) n(S) = 6 1326 = 1 221

P(E)=n(E)n(S)=61326=1221

Subject: Probability - Quantitative Aptitude - Arithmetic Ability

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## Two cards are drawn together at random from a pack of 52 cards. What is the probability that the second card is a queen?

Answer (1 of 9): 1/13. There are 4 queens and 52 cards. You don’t care what card is drawn the first time, so we needn’t worry about it. 4/52 reduces to 1/13. But if you like, let’s look at it the hard way. The first card drawn A) is a queen 4/52 the time. If it is, the chance of the second car...

Two cards are drawn together at random from a pack of 52 cards. What is the probability that the second card is a queen?

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Author has 463 answers and 245.3K answer views3y

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Two cards are drawn at random from a deck of cards. What is the probability of the second card being a queen?

As we are not told if the cards drawn are seen or not, I assume it is not relevant.

For that to be true this experiment must be one in a series of trials.

If you repeat this experiment 52 times, on average in 48 times the first card will not be queen.

The chance on the second one being a queen is then 4/51.

In 4 times on average the first card will be a queen. The chance on the second card being a queen is then 3/51.

So we get (48* (4/51) + 4* (3/51)) / 52=1/13.

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Two cards are drawn at random from a deck of cards. What is the probability of the second card being a queen?

There are 52 x 51 = 2652 ways you can pick two cards from a deck of 52 cards without replacement. The number of ways you can have a queen as the second card and not a queen as the first card is 4 x 48 = 192; the number of ways you can have 2 queens out of 4 is 4!/2! = 12; so the total number of ways to have a queen as the second card is 192 + 12 = 204; and probability is 204/2652 ~= 0.077.

An alternate approach to the solution is: Probability of both cards being queens is (4/52) * (3/51) = 12/2652. The probability of getting a queen on only the second card is (48/52)*(4/51) = 192/2652. Since yo

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Here is the math to verify Brian’s answer.

P(2nd card a queen) = P(1st card is a Queen) X P(2nd card is another Queen) + P(1st card is not a Queen) X P(2nd card is a Queen).

= 4/52 X 3/51 (4 queens out of 52 X 3 queens left out of 51) +

48/52 X 4/51 ( 48 not queens out of 52 X 4 Queens left out of 51)

= (12+ 192) /52 X 51

= 1/13 Lance Berg

Author has 18.9K answers and 28.6M answer views2y

1/13. There are 4 queens and 52 cards. You don’t care what card is drawn the first time, so we needn’t worry about it. 4/52 reduces to 1/13.

But if you like, let’s look at it the hard way.

The first card drawn

A) is a queen 4/52 the time. If it is, the chance of the second card being a queen is 3/51, so the chance of this occurring is 12/2652 (deliberately not reduced for ease of latter addition)

B) is not a queen 48/52 the time. If it is not, the chance of the second card being a queen is 4/51, so the chance of this occurring is 192/2652 (deliberately not reduced for ease of latter addition)

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What do you mean by 2nd card, when the two cards are drawn together ? . If you want the prob. of the event that at least one of the two cards be queen card then it is = 1 - pr(none of the two cards be a queen card)

= 1- {C(48,2)/ C(52, 2)}

= 1 - {(48 ×47)/2}/{(52 × 51)/2} = 0·14932 .

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Giovanni Mz

Former Chemical Engineer 3y

If the cards are drawn together, then there is no second card… both cards are the first drawn and the possibility that either one is a queen is (4+4)/52

Guys, does anyone know the answer?