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From a pack of cards, if three cards are drawn at random one after the other with replacement, find the probability that one is ace, one is jack and one is queen?
- a)16/7725
- b)16/5525
- c)18/5524
- d)64/5515
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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From a pack of cards, if three cards are drawn at random one after the...
(4c1 + 4c1 + 4c1)/(52c3)
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From a pack of cards, if three cards are drawn at random one after the...
To find the probability that one card is an ace, one card is a jack, and one card is a queen, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When drawing a card with replacement, there are 52 possible outcomes for each card drawn. Therefore, the total number of possible outcomes for drawing three cards with replacement is 52 x 52 x 52 = 140,608.
Number of favorable outcomes:
To determine the number of favorable outcomes, we need to consider the different possibilities for the arrangement of the ace, jack, and queen.
1. Ace, jack, queen: There are 4 aces, 4 jacks, and 4 queens in a deck of cards. The probability of drawing an ace, a jack, and a queen in any order is (4/52) x (4/52) x (4/52) = 64/140,608.
2. Jack, queen, ace: Similarly, the probability of drawing a jack, a queen, and an ace in any order is also 64/140,608.
3. Queen, ace, jack: The probability of drawing a queen, an ace, and a jack in any order is also 64/140,608.
Therefore, the total number of favorable outcomes is 64 + 64 + 64 = 192.
Probability calculation:
The probability is given by the ratio of favorable outcomes to total outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 192 / 140,608
Probability = 16 / 11,032
Simplifying the fraction, we get:
Probability = 16 / 11,032 = 4 / 2,758 = 2 / 1,379
Therefore, the correct answer is option B) 16/5525.
Total number of outcomes:
When drawing a card with replacement, there are 52 possible outcomes for each card drawn. Therefore, the total number of possible outcomes for drawing three cards with replacement is 52 x 52 x 52 = 140,608.
Number of favorable outcomes:
To determine the number of favorable outcomes, we need to consider the different possibilities for the arrangement of the ace, jack, and queen.
1. Ace, jack, queen: There are 4 aces, 4 jacks, and 4 queens in a deck of cards. The probability of drawing an ace, a jack, and a queen in any order is (4/52) x (4/52) x (4/52) = 64/140,608.
2. Jack, queen, ace: Similarly, the probability of drawing a jack, a queen, and an ace in any order is also 64/140,608.
3. Queen, ace, jack: The probability of drawing a queen, an ace, and a jack in any order is also 64/140,608.
Therefore, the total number of favorable outcomes is 64 + 64 + 64 = 192.
Probability calculation:
The probability is given by the ratio of favorable outcomes to total outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 192 / 140,608
Probability = 16 / 11,032
Simplifying the fraction, we get:
Probability = 16 / 11,032 = 4 / 2,758 = 2 / 1,379
Therefore, the correct answer is option B) 16/5525.
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