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4 – digit number greater than 5000 are randomly formed from the digits 0, 2, 3, 5 and 7. The probability of forming a number divisible by 5 when the digits are repeated is ______
Correct answer is '0.39-0.4'. Can you explain this answer?
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4 – digit number greater than 5000 are randomly formed from the ...
For a number to be greater than 5000, d1 should be filled with either 5 or 7
∴ Total numbers formed when the digits are repeated = 2 × 5 × 5 × 5 = 250
total cases = 250 -1 = 249 ( case of 5000 is not included)
Now, For the number to be divisible by 5, unit digit d4 should be either 0 or 5.
∴ Total no. of ways = 2 × 5 × 5 × 2 = 100
favorable cases = 100 - 1=9 ( 5000 is not included))
∴Required Probability = 
=0.397
=0.397Most Upvoted Answer
4 – digit number greater than 5000 are randomly formed from the ...
Calculating the probability of forming a number divisible by 5:
1. Total number of 4-digit numbers greater than 5000:
- Since the number has to be greater than 5000, the first digit can only be 5 or 7.
- For the first digit:
- There are 2 choices (5 or 7).
- For the remaining 3 digits:
- Each digit can be any of the 5 given digits (0, 2, 3, 5, 7).
- So, there are 5 choices for each of the 3 remaining digits.
- Total number of 4-digit numbers greater than 5000 = 2 choices * 5 choices * 5 choices * 5 choices = 250 numbers
2. Finding the numbers divisible by 5:
- For a number to be divisible by 5, the last digit must be either 0 or 5.
- For the last digit:
- There are 2 choices (0 or 5).
- For the remaining 3 digits:
- Each digit can be any of the 5 given digits (0, 2, 3, 5, 7).
- So, there are 5 choices for each of the 3 remaining digits.
- Total number of 4-digit numbers divisible by 5 = 2 choices * 5 choices * 5 choices * 5 choices = 250 numbers
3. Calculating the probability:
- Probability = Number of favorable outcomes / Total number of outcomes
- Probability = 250 / 625 (250 favorable outcomes out of the total 625 outcomes)
- Probability = 0.4
Therefore, the probability of forming a 4-digit number greater than 5000 that is divisible by 5 when the digits are repeated is approximately 0.4 or 40%.
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4 – digit number greater than 5000 are randomly formed from the digits 0, 2, 3, 5 and 7. The probability of forming a number divisible by 5 when the digits are repeated is ______Correct answer is '0.39-0.4'. Can you explain this answer?
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