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From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by.
- a)21/216
- b)19/316
- c)1/4
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
From eighty cards numbered 1 to 80, two cards are selected randomly. ...
Understanding the Problem
To find the probability that both selected cards have numbers divisible by 4, we first need to determine how many such cards exist and the total number of ways to select two cards from the total.
Total Cards
- There are 80 cards numbered from 1 to 80.
Cards Divisible by 4
- The numbers divisible by 4 within this range are: 4, 8, 12, ..., 80.
- To find how many numbers are divisible by 4, we can divide 80 by 4.
- There are 20 numbers (4 * 20 = 80) that are divisible by 4.
Total Ways to Select Two Cards
- The total number of ways to select 2 cards from 80 is calculated using the combination formula:
- Total combinations = C(80, 2) = 80! / (2!(80-2)!) = 3160.
Ways to Select Two Cards Divisible by 4
- The number of ways to select 2 cards from the 20 that are divisible by 4 is:
- Combinations = C(20, 2) = 20! / (2!(20-2)!) = 190.
Calculating the Probability
- The probability (P) that both selected cards are divisible by 4 is given by:
P = (Number of favorable outcomes) / (Total outcomes)
P = 190 / 3160 = 19 / 316.
Conclusion
The probability that both selected cards have numbers divisible by 4 is indeed 19/316, which corresponds to option 'B'.
To find the probability that both selected cards have numbers divisible by 4, we first need to determine how many such cards exist and the total number of ways to select two cards from the total.
Total Cards
- There are 80 cards numbered from 1 to 80.
Cards Divisible by 4
- The numbers divisible by 4 within this range are: 4, 8, 12, ..., 80.
- To find how many numbers are divisible by 4, we can divide 80 by 4.
- There are 20 numbers (4 * 20 = 80) that are divisible by 4.
Total Ways to Select Two Cards
- The total number of ways to select 2 cards from 80 is calculated using the combination formula:
- Total combinations = C(80, 2) = 80! / (2!(80-2)!) = 3160.
Ways to Select Two Cards Divisible by 4
- The number of ways to select 2 cards from the 20 that are divisible by 4 is:
- Combinations = C(20, 2) = 20! / (2!(20-2)!) = 190.
Calculating the Probability
- The probability (P) that both selected cards are divisible by 4 is given by:
P = (Number of favorable outcomes) / (Total outcomes)
P = 190 / 3160 = 19 / 316.
Conclusion
The probability that both selected cards have numbers divisible by 4 is indeed 19/316, which corresponds to option 'B'.
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Community Answer
From eighty cards numbered 1 to 80, two cards are selected randomly. ...
Total no. of numbers divisible by 4 between 1 to 80
80 = 4 + (n – 1)4
80 = 4n
⇒ n = 20
∴ Required Probability = 20C2 / 80C2 = 19/316
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From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by.a)21/216b)19/316c)1/4d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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