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All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is
- a)1/13
- b)12/13
- c)4/13
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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All the spades are taken out from a pack of cards. From these cards, c...
So the required probability that are comes in 4th draw
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All the spades are taken out from a pack of cards. From these cards, c...
Probability of drawing the ace of spades in the 4th draw
To find the probability of drawing the ace of spades in the 4th draw, let's break down the problem step by step.
Step 1: Determine the number of cards in the pack.
Since all the spades have been removed from the pack, we are left with 52 - 13 = 39 cards.
Step 2: Determine the total number of ways to draw 4 cards without replacement.
In the first draw, we have 39 options. In the second draw, we have 38 options (as one card has already been drawn). In the third draw, we have 37 options, and in the fourth draw, we have 36 options.
Therefore, the total number of ways to draw 4 cards without replacement is 39 * 38 * 37 * 36.
Step 3: Determine the number of favorable outcomes.
To find the number of favorable outcomes (i.e., the number of ways the ace of spades can be drawn in the 4th draw), we need to consider the possibilities in the first three draws.
In the first draw, there are no spades, so the ace of spades cannot be drawn.
In the second draw, there are still no spades, so the ace of spades cannot be drawn.
In the third draw, there are still no spades, so the ace of spades cannot be drawn.
In the fourth draw, there is only one ace of spades left in the pack, so the ace of spades can be drawn in only one way.
Therefore, the number of favorable outcomes is 1.
Step 4: Calculate the probability.
The probability of drawing the ace of spades in the 4th draw is given by the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / (39 * 38 * 37 * 36)
= 1 / 62,596.
Simplifying the fraction, we get:
Probability = 1/13
Therefore, the probability of drawing the ace of spades in the 4th draw is 1/13.
To find the probability of drawing the ace of spades in the 4th draw, let's break down the problem step by step.
Step 1: Determine the number of cards in the pack.
Since all the spades have been removed from the pack, we are left with 52 - 13 = 39 cards.
Step 2: Determine the total number of ways to draw 4 cards without replacement.
In the first draw, we have 39 options. In the second draw, we have 38 options (as one card has already been drawn). In the third draw, we have 37 options, and in the fourth draw, we have 36 options.
Therefore, the total number of ways to draw 4 cards without replacement is 39 * 38 * 37 * 36.
Step 3: Determine the number of favorable outcomes.
To find the number of favorable outcomes (i.e., the number of ways the ace of spades can be drawn in the 4th draw), we need to consider the possibilities in the first three draws.
In the first draw, there are no spades, so the ace of spades cannot be drawn.
In the second draw, there are still no spades, so the ace of spades cannot be drawn.
In the third draw, there are still no spades, so the ace of spades cannot be drawn.
In the fourth draw, there is only one ace of spades left in the pack, so the ace of spades can be drawn in only one way.
Therefore, the number of favorable outcomes is 1.
Step 4: Calculate the probability.
The probability of drawing the ace of spades in the 4th draw is given by the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / (39 * 38 * 37 * 36)
= 1 / 62,596.
Simplifying the fraction, we get:
Probability = 1/13
Therefore, the probability of drawing the ace of spades in the 4th draw is 1/13.
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All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw isa)1/13b)12/13c)4/13d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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