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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?
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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).
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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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DIRECTIONS for the question: Read the information given below and answer the question that follows.Teams from seven states – Andhra Pradesh, Bihar, Gujrat, Madhya Pradesh, Maharashtra, Uttar Pradesh and West Bengal – are participating in the national basketball championship. After the inauguration ceremony, the reporter from 11 Sports spoke to nine players – Akshay Kumar, Anil Thakur, David D’Souza, Jayesh Patel, Rahul Jha, Rajeev Sinha, Ramesh Nayudu, Sachdev Sharma and Subhash Divyundu – from these seven teams. Additional information about the interviews is as follows. Each player interviewed wore a jersey with a unique number. David D’Souza with jersey number 31 plays for Andhra Pradesh and is also known as a 3-pointer. Rajeev Sinha with jersey number 23 is the eldest player and Subhash Divyundu is the heaviest player. Sachdev Sharma has jersey number 30, while Jayesh Patel has jersey number 40. Rahul Jha is one of the dunkers and he is from West Bengal. The player from UP and one player from Andhra Pradesh have single digit jersey numbers. Both the players with jersey numbers 40 and 34 play for Gujrat. Rahul Jha was interviewed after Ramesh Nayudu, but was not the last player to be interviewed. Both the players from Andhra Pradesh were interviewed one after the other and they were followed by both players from Gujrat. The players from Uttar Pradesh, Maharashtra and West Bengal were interviewed one after the other in that order. The player with jersey number 23 plays for Bihar. The heaviest player has jersey number 34. Ramesh Nayudu is a passer for Andhra Pradesh. Jersey numbers 2 and 3 were the only single digit jersey numbers. The player from Maharashtra was interviewed 7th.Q.If David D’Souza was the first to be interviewed, who could not be interviewed 2nd?

DIRECTIONS for the question: Read the information given below and answer the question that follows.Teams from seven states – Andhra Pradesh, Bihar, Gujrat, Madhya Pradesh, Maharashtra, Uttar Pradesh and West Bengal – are participating in the national basketball championship. After the inauguration ceremony, the reporter from 11 Sports spoke to nine players – Akshay Kumar, Anil Thakur, David D’Souza, Jayesh Patel, Rahul Jha, Rajeev Sinha, Ramesh Nayudu, Sachdev Sharma and Subhash Divyundu – from these seven teams. Additional information about the interviews is as follows. Each player interviewed wore a jersey with a unique number. David D’Souza with jersey number 31 plays for Andhra Pradesh and is also known as a 3-pointer. Rajeev Sinha with jersey number 23 is the eldest player and Subhash Divyundu is the heaviest player. Sachdev Sharma has jersey number 30, while Jayesh Patel has jersey number 40. Rahul Jha is one of the dunkers and he is from West Bengal. The player from UP and one player from Andhra Pradesh have single digit jersey numbers. Both the players with jersey numbers 40 and 34 play for Gujrat. Rahul Jha was interviewed after Ramesh Nayudu, but was not the last player to be interviewed. Both the players from Andhra Pradesh were interviewed one after the other and they were followed by both players from Gujrat. The players from Uttar Pradesh, Maharashtra and West Bengal were interviewed one after the other in that order. The player with jersey number 23 plays for Bihar. The heaviest player has jersey number 34. Ramesh Nayudu is a passer for Andhra Pradesh. Jersey numbers 2 and 3 were the only single digit jersey numbers. The player from Maharashtra was interviewed 7th.Q.If Anil Thakur, Akshay Kumar and Sachdev Sharma were players who got interviewed in order, then who will not be wearing Jersey number 2?

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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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