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30 Jun 2025, 09:14
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Answer
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Explanation
This is a classic probability problem where the core logic is based on symmetry.
Core Logic:
Let n be the total number of integers in the set (from x to y).
There are three possible outcomes when Ann and Bob pick a number:
By symmetry, the probability that Ann wins is the exact same as the probability that Bob wins.
P(Ann wins) + P(Bob wins) + P(Tie) = 1
2 * P(Ann wins) + P(Tie) = 1
The probability of a tie is the chance they pick the same number. There are n numbers to choose from, so the probability of a tie is 1/n.
So, 2 * P(Ann wins) + 1/n = 1. This means if we can find a single value for n (the total number of integers), we can solve the problem. The number of integers is n = y - x + 1.
Analyzing the Statements:
Because only statement (1) is sufficient, the answer is A.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Explanation
This is a classic probability problem where the core logic is based on symmetry.
Core Logic:
Let n be the total number of integers in the set (from x to y).
There are three possible outcomes when Ann and Bob pick a number:
- Ann's number > Bob's number (Ann wins)
- Bob's number > Ann's number (Bob wins)
- Ann's number = Bob's number (They tie)
By symmetry, the probability that Ann wins is the exact same as the probability that Bob wins.
P(Ann wins) + P(Bob wins) + P(Tie) = 1
2 * P(Ann wins) + P(Tie) = 1
The probability of a tie is the chance they pick the same number. There are n numbers to choose from, so the probability of a tie is 1/n.
So, 2 * P(Ann wins) + 1/n = 1. This means if we can find a single value for n (the total number of integers), we can solve the problem. The number of integers is n = y - x + 1.
Analyzing the Statements:
- Statement (1): y - x = 9
This gives us the range. We can find the number of integers:
n = (y - x) + 1 = 9 + 1 = 10.
Since we have a specific value for n, we can find the exact probability.
This statement is SUFFICIENT.
- Statement (2): y = -20
This only tells us the last integer in the set. We don't know the first integer, x.
n = y - x + 1 = -20 - x + 1 = -19 - x.
Since x could be any integer less than or equal to -20, we cannot find a single value for n.
This statement is INSUFFICIENT.
Because only statement (1) is sufficient, the answer is A.
30 Jun 2025, 09:15
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lets A= anns no, B = Bobs no.
we need to find P(A>B)
Statement 1=>
y-x = 9 that mean n=10= total no
total combination possible = 10*10 = 100
here there are three possibilities A>B, A<B and A=B
A=B = 10 as there are 10 no
A>B and A<B = 45 equal possibilities
so we can find P(A>B) Sufficient
Statement 2 =>
y = -20 but we don't have value of x so we don't know the total numbers. so Not Sufficient
we need to find P(A>B)
Statement 1=>
y-x = 9 that mean n=10= total no
total combination possible = 10*10 = 100
here there are three possibilities A>B, A<B and A=B
A=B = 10 as there are 10 no
A>B and A<B = 45 equal possibilities
so we can find P(A>B) Sufficient
Statement 2 =>
y = -20 but we don't have value of x so we don't know the total numbers. so Not Sufficient
30 Jun 2025, 09:19
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To find the probability that Ann picks a number greater than Bob, we need to know how many integers are in the range. That number is n = y - x + 1. The formula for the probability will be (n - 1) / 2n.
Statement 1 : y - x = 9.
Since x and y are integers, n = 10. The probability is 9/20. Statement A alone is sufficient.
Statement 2 : y = -20
This doesn't tell us x. Without knowing x, we can't find n or the probability. Statement B alone is not sufficient.
Answer is A.
Statement 1 : y - x = 9.
Since x and y are integers, n = 10. The probability is 9/20. Statement A alone is sufficient.
Statement 2 : y = -20
This doesn't tell us x. Without knowing x, we can't find n or the probability. Statement B alone is not sufficient.
Answer is A.
