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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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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}
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Ten cards numbered 1 through 10 are placed in a box, mixed up thorough...
To solve this problem, we can use the concept of conditional probability. We are given that one card has been drawn from a box containing ten cards numbered 1 through 10, and we know that the number on the drawn card is more than 3. We need to find the probability that the drawn card is an even number.
Let's break down the problem step by step:
Step 1: Determine the sample space
The sample space is the set of all possible outcomes, which in this case is the numbers on the ten cards. So, the sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Step 2: Determine the event space
The event space is the set of outcomes that satisfy the given condition, which in this case is the numbers on the cards that are more than 3. So, the event space is {4, 5, 6, 7, 8, 9, 10}.
Step 3: Determine the favorable outcomes
The favorable outcomes are the outcomes that satisfy both conditions: being more than 3 and being an even number. So, the favorable outcomes are {4, 6, 8, 10}.
Step 4: Calculate the probability
The probability can be calculated using the formula:
P(A|B) = P(A ∩ B) / P(B)
Here, A represents the event of drawing an even number, and B represents the event of drawing a number more than 3.
P(A ∩ B) is the probability of drawing a number that is both even and more than 3, which is the number of favorable outcomes divided by the total number of outcomes in the sample space. In this case, P(A ∩ B) = 4/10 = 2/5.
P(B) is the probability of drawing a number more than 3, which is the number of outcomes in the event space divided by the total number of outcomes in the sample space. In this case, P(B) = 7/10.
Therefore, the probability of drawing an even number given that the number is more than 3 is:
P(A|B) = P(A ∩ B) / P(B) = (2/5) / (7/10) = (2/5) * (10/7) = 4/7.
Hence, the correct answer is option A: 4/7.
Let's break down the problem step by step:
Step 1: Determine the sample space
The sample space is the set of all possible outcomes, which in this case is the numbers on the ten cards. So, the sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Step 2: Determine the event space
The event space is the set of outcomes that satisfy the given condition, which in this case is the numbers on the cards that are more than 3. So, the event space is {4, 5, 6, 7, 8, 9, 10}.
Step 3: Determine the favorable outcomes
The favorable outcomes are the outcomes that satisfy both conditions: being more than 3 and being an even number. So, the favorable outcomes are {4, 6, 8, 10}.
Step 4: Calculate the probability
The probability can be calculated using the formula:
P(A|B) = P(A ∩ B) / P(B)
Here, A represents the event of drawing an even number, and B represents the event of drawing a number more than 3.
P(A ∩ B) is the probability of drawing a number that is both even and more than 3, which is the number of favorable outcomes divided by the total number of outcomes in the sample space. In this case, P(A ∩ B) = 4/10 = 2/5.
P(B) is the probability of drawing a number more than 3, which is the number of outcomes in the event space divided by the total number of outcomes in the sample space. In this case, P(B) = 7/10.
Therefore, the probability of drawing an even number given that the number is more than 3 is:
P(A|B) = P(A ∩ B) / P(B) = (2/5) / (7/10) = (2/5) * (10/7) = 4/7.
Hence, 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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