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15 Jul 2024, 09:41
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C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Probability of finding neither is 1- probability of finding 1 - probability of finding both. We have sufficient information to answer this question when we take both statements together but neither alone.
Probability of finding neither is 1- probability of finding 1 - probability of finding both. We have sufficient information to answer this question when we take both statements together but neither alone.
15 Jul 2024, 09:44
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In a science experiment, a mouse is placed in a labyrinth with two different treats hidden in it. What is the probability that the mouse will find neither of the treats?
(1) The probability that the mouse will find only one of the two treats is 1/5.
(2) The probability that the mouse will find both treats is 3/10.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Answer ->
Let probability that the mouse will find neither of the treats = P(N)
Let probability that the mouse will find only one of the two treats = P(1)
Let probability that the mouse will find both of the two treats = P(2)
Statement 1-
P(1) = 1/5
Not Sufficient
Statement 2-
P(2) = 3/10
Not Sufficient
Both -
1 = P(N) + P(1) + P(2)
1 = P(N) + 1/5 + 3/10
Sufficient
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
(1) The probability that the mouse will find only one of the two treats is 1/5.
(2) The probability that the mouse will find both treats is 3/10.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Answer ->
Let probability that the mouse will find neither of the treats = P(N)
Let probability that the mouse will find only one of the two treats = P(1)
Let probability that the mouse will find both of the two treats = P(2)
Statement 1-
P(1) = 1/5
Not Sufficient
Statement 2-
P(2) = 3/10
Not Sufficient
Both -
1 = P(N) + P(1) + P(2)
1 = P(N) + 1/5 + 3/10
Sufficient
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
15 Jul 2024, 09:57
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Let P(X) be probability of mouse finding first treat
Let P(Y) be the probability of mouse finding the second treat.
we need to find 1 - P (X OR Y)
Statement 1
P (X & Y') + P(X & Y') = 1/5
Not sufficient.
Statement 2
P (X & Y) = 3/10
Not sufficient.
1 & 2 TOGETHER
We know
P (X or Y ) = P(X)+P(Y)- P (X & Y)
= P(X&Y)+P (X&Y')+P(Y&X)+P(Y&X') - P (X&Y)
= P (X&Y) + P (X&Y') + P(Y&X')
= (3/10 )+ (1/5)
= 1/2
Hence, 1 - P (X OR Y) = 1 - 1/2 = 1/2
Hence sufficient. Answer C.
Let P(Y) be the probability of mouse finding the second treat.
we need to find 1 - P (X OR Y)
Statement 1
P (X & Y') + P(X & Y') = 1/5
Not sufficient.
Statement 2
P (X & Y) = 3/10
Not sufficient.
1 & 2 TOGETHER
We know
P (X or Y ) = P(X)+P(Y)- P (X & Y)
= P(X&Y)+P (X&Y')+P(Y&X)+P(Y&X') - P (X&Y)
= P (X&Y) + P (X&Y') + P(Y&X')
= (3/10 )+ (1/5)
= 1/2
Hence, 1 - P (X OR Y) = 1 - 1/2 = 1/2
Hence sufficient. Answer C.
