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From a deck of 52 cards, a card is selected and without replacing the card a new card is selected. Find out the probability that the first card is an ace and second card is a king ?
- a)4/52*3/51
- b)4/51*3/52
- c)4/52*4/51
- d)3/52*3/51
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
From a deck of 52 cards, a card is selected and without replacing the ...
After selecting first card, the rest cards are 51 so
Probability of first card is 4/52 and of second card is 4/51
Probability of first card is 4/52 and of second card is 4/51
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From a deck of 52 cards, a card is selected and without replacing the ...
Solution:
Given, a deck of 52 cards, a card is selected and without replacing the card a new card is selected.
We need to find out the probability that the first card is an ace and the second card is a king.
Total number of ways to draw two cards from a deck of 52 cards = 52C2
= (52 x 51) / (2 x 1)
= 1326
Let's calculate the probability of drawing an ace as the first card.
Number of aces in a deck of 52 cards = 4
Number of cards remaining after drawing an ace = 51
So, the probability of drawing an ace as the first card = 4/52
Now, for the second card to be a king, we have only 4 kings left in the deck of 51 cards.
So, the probability of drawing a king as the second card, given that the first card is an ace = 4/51
So, the probability of drawing an ace as the first card and a king as the second card = (4/52) x (4/51)
= 16/2652
= 4/663
= 0.006006
Therefore, the correct option is (C) 4/52 x 4/51.
Given, a deck of 52 cards, a card is selected and without replacing the card a new card is selected.
We need to find out the probability that the first card is an ace and the second card is a king.
Total number of ways to draw two cards from a deck of 52 cards = 52C2
= (52 x 51) / (2 x 1)
= 1326
Let's calculate the probability of drawing an ace as the first card.
Number of aces in a deck of 52 cards = 4
Number of cards remaining after drawing an ace = 51
So, the probability of drawing an ace as the first card = 4/52
Now, for the second card to be a king, we have only 4 kings left in the deck of 51 cards.
So, the probability of drawing a king as the second card, given that the first card is an ace = 4/51
So, the probability of drawing an ace as the first card and a king as the second card = (4/52) x (4/51)
= 16/2652
= 4/663
= 0.006006
Therefore, the correct option is (C) 4/52 x 4/51.
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