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Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number.
- a)4/7
- b)8/7
- c)6/7
- d)2/7
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Ten cards numbered 1 through 10 are placed in a box, mixed up thorough...
Let the events be :
A : Number on the card drawn is even.
B : Number on the card is more than 3.
We are to find P(A/B).
We have : S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8,10}
and B = {4, 5, 6, 7, 8, 9, 10}
A : Number on the card drawn is even.
B : Number on the card is more than 3.
We are to find P(A/B).
We have : S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8,10}
and B = {4, 5, 6, 7, 8, 9, 10}
Most Upvoted Answer
Ten cards numbered 1 through 10 are placed in a box, mixed up thorough...
To find the probability that the drawn card is an even number, given that it is more than 3, we first need to determine the sample space and the favorable outcomes.
**Sample Space:**
The sample space consists of all possible outcomes when one card is drawn from the box. Since there are 10 cards numbered 1 through 10, the sample space contains 10 elements.
**Favorable Outcomes:**
Since we know that the drawn card is more than 3, the favorable outcomes are the even numbers greater than 3, which are 4, 6, 8, and 10. There are a total of 4 favorable outcomes.
**Finding the Probability:**
The probability of an event is given by the ratio of favorable outcomes to the total number of outcomes in the sample space.
P(Even number | More than 3) = (Number of favorable outcomes)/(Total number of outcomes)
P(Even number | More than 3) = 4/10
Simplifying, we get:
P(Even number | More than 3) = 2/5
However, the question asks for the probability of an even number, given that the drawn card is more than 3. Therefore, we need to consider the event that the card is more than 3 as the new sample space.
**New Sample Space:**
The new sample space consists of all possible outcomes when one card is drawn from the box, given that it is more than 3. Since there are 7 cards greater than 3 (4, 5, 6, 7, 8, 9, 10), the new sample space contains 7 elements.
**New Favorable Outcomes:**
The favorable outcomes remain the same, as we are still interested in the even numbers greater than 3 (4, 6, 8, 10). There are still 4 favorable outcomes.
**Finding the Probability:**
Using the new sample space and favorable outcomes, we can calculate the probability again.
P(Even number | More than 3) = (Number of favorable outcomes)/(Total number of outcomes)
P(Even number | More than 3) = 4/7
Therefore, the correct answer is option 'A', 4/7.
**Sample Space:**
The sample space consists of all possible outcomes when one card is drawn from the box. Since there are 10 cards numbered 1 through 10, the sample space contains 10 elements.
**Favorable Outcomes:**
Since we know that the drawn card is more than 3, the favorable outcomes are the even numbers greater than 3, which are 4, 6, 8, and 10. There are a total of 4 favorable outcomes.
**Finding the Probability:**
The probability of an event is given by the ratio of favorable outcomes to the total number of outcomes in the sample space.
P(Even number | More than 3) = (Number of favorable outcomes)/(Total number of outcomes)
P(Even number | More than 3) = 4/10
Simplifying, we get:
P(Even number | More than 3) = 2/5
However, the question asks for the probability of an even number, given that the drawn card is more than 3. Therefore, we need to consider the event that the card is more than 3 as the new sample space.
**New Sample Space:**
The new sample space consists of all possible outcomes when one card is drawn from the box, given that it is more than 3. Since there are 7 cards greater than 3 (4, 5, 6, 7, 8, 9, 10), the new sample space contains 7 elements.
**New Favorable Outcomes:**
The favorable outcomes remain the same, as we are still interested in the even numbers greater than 3 (4, 6, 8, 10). There are still 4 favorable outcomes.
**Finding the Probability:**
Using the new sample space and favorable outcomes, we can calculate the probability again.
P(Even number | More than 3) = (Number of favorable outcomes)/(Total number of outcomes)
P(Even number | More than 3) = 4/7
Therefore, the correct answer is option 'A', 4/7.
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Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number.a)4/7b)8/7c)6/7d)2/7Correct answer is option 'A'. Can you explain this answer?
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