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A bag contains 50 tickets numbered 51,52,???,100 of which 5 are drawn and arranged in ascending order of magnitude.find the probability that the third number is 80.
- a)551/312500
- b)551/15134
- c)340/15134
- d)3364/31250030856/3125000
- e)30856/3125000
Correct answer is option 'B'. Can you explain this answer?
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A bag contains 50 tickets numbered 51,52,???,100 of which 5 are drawn ...
To solve this problem, we need to determine the total number of possible outcomes and the number of favorable outcomes in order to calculate the probability.
Total Number of Possible Outcomes:
There are 50 tickets numbered from 51 to 100 in the bag. We need to draw 5 tickets, so the total number of possible outcomes can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
In this case, n = 50 and r = 5. Plugging in these values, we get:
50C5 = 50! / (5!(50-5)!) = 2,118,760
Therefore, there are 2,118,760 possible outcomes.
Number of Favorable Outcomes:
We want to find the probability that the third number drawn is 80. Since the numbers are arranged in ascending order, the first two numbers must be less than 80.
The first number can be any number from 51 to 79, which gives us 29 possible choices. The second number can be any number from the remaining tickets, which is 28 tickets. The third number must be 80. The fourth number can be any number from the remaining tickets, which is 20 tickets. The fifth number can be any number from the remaining tickets, which is 19 tickets.
Therefore, the number of favorable outcomes is:
29 * 28 * 1 * 20 * 19 = 30856
Calculating the Probability:
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 30856 / 2,118,760
Simplifying this fraction, we get:
Probability = 551/15134
Therefore, the correct answer is option B.
Total Number of Possible Outcomes:
There are 50 tickets numbered from 51 to 100 in the bag. We need to draw 5 tickets, so the total number of possible outcomes can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
In this case, n = 50 and r = 5. Plugging in these values, we get:
50C5 = 50! / (5!(50-5)!) = 2,118,760
Therefore, there are 2,118,760 possible outcomes.
Number of Favorable Outcomes:
We want to find the probability that the third number drawn is 80. Since the numbers are arranged in ascending order, the first two numbers must be less than 80.
The first number can be any number from 51 to 79, which gives us 29 possible choices. The second number can be any number from the remaining tickets, which is 28 tickets. The third number must be 80. The fourth number can be any number from the remaining tickets, which is 20 tickets. The fifth number can be any number from the remaining tickets, which is 19 tickets.
Therefore, the number of favorable outcomes is:
29 * 28 * 1 * 20 * 19 = 30856
Calculating the Probability:
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 30856 / 2,118,760
Simplifying this fraction, we get:
Probability = 551/15134
Therefore, the correct answer is option B.
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A bag contains 50 tickets numbered 51,52,???,100 of which 5 are drawn and arranged in ascending order of magnitude.find the probability that the third number is 80.a)551/312500b)551/15134c)340/15134d)3364/31250030856/3125000e)30856/3125000Correct answer is option 'B'. Can you explain this answer?
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