Question

two cards are drawn from a deck of 52 cards whithout replacement what is the probability of getting both cards black or one card queen and other king​

Answer 1

Step-by-step explanation:

There are 26 black cards in a deck of 52 cards.

Let P(A) be the probability of getting a black card in the first draw.

∴P(A)=

52

26

=

2

1

Let P(B) be the probability of getting a black card on the second draw.

Since the card is not replaced,

∴P(B)=

51

25

Thus, probability of getting both the cards black =

2

1

×

51

25

=

102

25

=0.24.

Answer 2

The given question is two cards drawn from a deck of 52 cards without replacement.

we have to find the probability of getting both cards black or one card queen and another king

In a deck of 52 cards, there are 26 black, 26 red cards, 4 kings and 4 queens.

The probability of drawing the black card in the deck of cards is,

there will be 26 black cards

$\frac{26}{52}$

The second card should be drawn, now without replacement, there will be 51 cards in total and 25 black cards.

The probability of getting a black card without replacement is

$\frac{25}{51}$

The probability of getting both cards black will be

$\frac{26}{52} \times \frac{25}{51} = 0.245$

Then we have to find the probability of drawing a king and a queen card.

There are two cases available for this, they are

If a king is drawn first the probability will be

$\frac{4}{52}$

Then the Queen will be drawn in the second time the probability will be

$\frac{4}{51}$

The probability of herring king in a first draw and queen in a second draw will be

$\frac{4}{51} \times \frac{4}{52} = \frac{4}{663}$

likewise, vice versa getting queen in the first draw and king in the second draw will be

$\frac{4}{52} \times \frac{4}{51} = \frac{4}{663}$

The probability of getting king and queen will be

probability of King in first and Queen in second draw + probability of queen in first and King in the second draw

$\frac{4}{663} + \frac{4}{663} = \frac{8}{663}$

$\frac{8}{663} = 0.012$

Therefore, the final probability of getting both cards black or one card queen and another king will be

$0.245 + 0.012= 0.0257$

Therefore, the final answer to the given question is 0.0257.

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