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The probability of a Ramesh scoring more than 75 in an exam is 20%. What is the minimum number of times he should take the exam to have 50% chance of scoring more than 75?
- a)4
- b)2
- c)3
- d)6
- e)8
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The probability of a Ramesh scoring more than 75 in an exam is 20%. W...
To find the minimum number of times Ramesh should take the exam to have a 50% chance of scoring more than 75, we can use the concept of probability and complementary probability.
Let's assume that the probability of Ramesh scoring more than 75 in a single exam is p = 0.2 (or 20%).
The probability of Ramesh not scoring more than 75 in a single exam is q = 1 - p = 1 - 0.2 = 0.8 (or 80%).
Finding the probability of not scoring more than 75 in n exams:
The probability of not scoring more than 75 in a single exam is q = 0.8.
The probability of not scoring more than 75 in n exams is q^n, as these events are independent.
Now, let's find the minimum value of n such that the probability of not scoring more than 75 in n exams is less than or equal to 0.5.
0.8^n ≤ 0.5
Taking the logarithm of both sides:
log(0.8^n) ≤ log(0.5)
n * log(0.8) ≤ log(0.5)
n ≥ log(0.5) / log(0.8)
Using logarithmic properties, we can simplify this:
n ≥ log(0.5) / log(0.8) ≈ 3.3219
Since the number of exams must be an integer, we take the smallest integer greater than or equal to this value, which is 4.
Therefore, the minimum number of times Ramesh should take the exam to have a 50% chance of scoring more than 75 is 4.
Hence, the correct answer is option 'A' (4).
Let's assume that the probability of Ramesh scoring more than 75 in a single exam is p = 0.2 (or 20%).
The probability of Ramesh not scoring more than 75 in a single exam is q = 1 - p = 1 - 0.2 = 0.8 (or 80%).
Finding the probability of not scoring more than 75 in n exams:
The probability of not scoring more than 75 in a single exam is q = 0.8.
The probability of not scoring more than 75 in n exams is q^n, as these events are independent.
Now, let's find the minimum value of n such that the probability of not scoring more than 75 in n exams is less than or equal to 0.5.
0.8^n ≤ 0.5
Taking the logarithm of both sides:
log(0.8^n) ≤ log(0.5)
n * log(0.8) ≤ log(0.5)
n ≥ log(0.5) / log(0.8)
Using logarithmic properties, we can simplify this:
n ≥ log(0.5) / log(0.8) ≈ 3.3219
Since the number of exams must be an integer, we take the smallest integer greater than or equal to this value, which is 4.
Therefore, the minimum number of times Ramesh should take the exam to have a 50% chance of scoring more than 75 is 4.
Hence, the correct answer is option 'A' (4).
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Community Answer
The probability of a Ramesh scoring more than 75 in an exam is 20%. W...
Chances of not scoring 75 = 0.8
Chances of not scoring 75 in 1st n attempts = (0.8)n
So, we need to find 1 - 0.8n > 0.5
Or, 0.8n < />
The smallest value of n for which this is true is 4.
So, Ramesh must take the exam at least 4 times to have 50% chance of scoring more than 75.
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The probability of a Ramesh scoring more than 75 in an exam is 20%. What is the minimum number of times he should take the exam to have 50% chance of scoring more than 75?a)4b)2c)3d)6e)8Correct answer is option 'A'. Can you explain this answer?
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