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From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace?
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From a well shuffled pack of cards two cards are drawn one after the o...
**Probability of drawing cards with replacement:**
When drawing cards with replacement, it means that after each draw, the card is placed back into the deck and the deck is shuffled again. This means that the probability of drawing a specific card remains the same for each draw.
**Probability of drawing a Diamond and then a Spade:**
There are 13 Diamonds in a deck of cards, so the probability of drawing a Diamond on the first draw is 13/52. After replacing the card, the probability of drawing a Spade on the second draw is also 13/52.
Therefore, the probability of drawing a Diamond and then a Spade is (13/52) * (13/52) = 169/2704.
**Probability of drawing a King and then a Queen:**
There are 4 Kings and 4 Queens in a deck of cards, so the probability of drawing a King on the first draw is 4/52. After replacing the card, the probability of drawing a Queen on the second draw is also 4/52.
Therefore, the probability of drawing a King and then a Queen is (4/52) * (4/52) = 16/2704.
**Probability of drawing two cards from the same suit:**
There are 4 suits in a deck of cards (Diamonds, Hearts, Clubs, and Spades), each with 13 cards.
To calculate the probability of drawing two cards from the same suit, we need to consider two cases: drawing two cards from the same suit and drawing two cards from different suits.
- Drawing two cards from the same suit: There are 4 suits to choose from, and once a suit is chosen, there are 13 cards of that suit. So, the probability of drawing two cards from the same suit is (4/52) * (13/51) = 52/2652.
- Drawing two cards from different suits: There are 4 suits to choose from for the first card, and once a suit is chosen, there are 3 suits left for the second card. So, the probability of drawing two cards from different suits is (4/52) * (39/51) = 156/2652.
Therefore, the probability of drawing two cards from the same suit is 52/2652 + 156/2652 = 208/2652.
**Probability of drawing at least one Ace:**
There are 4 Aces in a deck of cards, so the probability of drawing at least one Ace can be calculated by subtracting the probability of not drawing any Ace from 1.
- Probability of not drawing any Ace: There are 48 non-Ace cards in a deck of cards, so the probability of not drawing any Ace on the first draw is 48/52. After replacing the card, the probability of not drawing any Ace on the second draw is also 48/52.
Therefore, the probability of not drawing any Ace is (48/52) * (48/52) = 2304/2704.
- Probability of drawing at least one Ace: 1 - 2304/2704 = 400/2704.
Therefore, the probability of drawing at least one Ace is 400/2704.
By following these steps, you can calculate the probabilities of different events when drawing cards with replacement.
When drawing cards with replacement, it means that after each draw, the card is placed back into the deck and the deck is shuffled again. This means that the probability of drawing a specific card remains the same for each draw.
**Probability of drawing a Diamond and then a Spade:**
There are 13 Diamonds in a deck of cards, so the probability of drawing a Diamond on the first draw is 13/52. After replacing the card, the probability of drawing a Spade on the second draw is also 13/52.
Therefore, the probability of drawing a Diamond and then a Spade is (13/52) * (13/52) = 169/2704.
**Probability of drawing a King and then a Queen:**
There are 4 Kings and 4 Queens in a deck of cards, so the probability of drawing a King on the first draw is 4/52. After replacing the card, the probability of drawing a Queen on the second draw is also 4/52.
Therefore, the probability of drawing a King and then a Queen is (4/52) * (4/52) = 16/2704.
**Probability of drawing two cards from the same suit:**
There are 4 suits in a deck of cards (Diamonds, Hearts, Clubs, and Spades), each with 13 cards.
To calculate the probability of drawing two cards from the same suit, we need to consider two cases: drawing two cards from the same suit and drawing two cards from different suits.
- Drawing two cards from the same suit: There are 4 suits to choose from, and once a suit is chosen, there are 13 cards of that suit. So, the probability of drawing two cards from the same suit is (4/52) * (13/51) = 52/2652.
- Drawing two cards from different suits: There are 4 suits to choose from for the first card, and once a suit is chosen, there are 3 suits left for the second card. So, the probability of drawing two cards from different suits is (4/52) * (39/51) = 156/2652.
Therefore, the probability of drawing two cards from the same suit is 52/2652 + 156/2652 = 208/2652.
**Probability of drawing at least one Ace:**
There are 4 Aces in a deck of cards, so the probability of drawing at least one Ace can be calculated by subtracting the probability of not drawing any Ace from 1.
- Probability of not drawing any Ace: There are 48 non-Ace cards in a deck of cards, so the probability of not drawing any Ace on the first draw is 48/52. After replacing the card, the probability of not drawing any Ace on the second draw is also 48/52.
Therefore, the probability of not drawing any Ace is (48/52) * (48/52) = 2304/2704.
- Probability of drawing at least one Ace: 1 - 2304/2704 = 400/2704.
Therefore, the probability of drawing at least one Ace is 400/2704.
By following these steps, you can calculate the probabilities of different events when drawing cards with replacement.
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From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace?
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From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace?.
From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a well shuffled pack of cards two cards are drawn one after the other (a) with replacement (b) without replacement. Find the probability that (1)The first card is Diamond and other is spade(2) one of them is a king and other is a queen (3) both the cards are from the same suit (4) atleast one of them is an ace?.
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