Ans: B
P(b) = B/Total
now State: 1) gives info about total only so not suffi.

Stat 2) Ration of B: G = 7:5 means B= 7T/12 and G =5T/12 total = T
P(B) = (7T/12)/T so the probablity is 7/12 (Suffi)


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(1) There are 480 students at Learngood.
No info about B:G ratio
Insufficient

(2) At Learngood, the ratio of boys to girls is 7:5
Given ratio = 7 / 5
Hence, The Probability = 7 / 7 + 5 = 7 / 12
Sufficient

Hence, B.
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Solution

Given:

• At Learngood Elementary, one of the students is randomly selected

To find:

• The probability that the selected student will be a boy

Analysing Statement 1

• As per the information given in statement 1, there are 480 students in total.

o However, among those 480 students, we don’t know how many boys and how many girls
• Therefore, we can’t find the probability of selecting a boy

Hence, statement 1 is not sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, the ratio of boys to girls is 7:5

o We can assume the number of boys is 7x and girls 5x
o Hence, the probability of selecting a boy = \(\frac{7x}{7x + 5x}\) = \(\frac{7}{12}\)
• So, from statement 2, we can find the probability

Hence, the correct answer is option B.

Answer: B
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Target question: What is the probability that the (selected) student will be a boy?

Statement 1: There are 480 students at Learngood.
Since we have no information about the number of boys at the school, statement 1 is NOT SUFFICIENT

Statement 2: At Learngood, the ratio of boys to girls is 7:5
This tells us that, for every 12 children at the school, 7 are boys, and 5 are girls.
In other words, 7/12 of the students at the school are boys, which means P(selected student is a boy) = 7/12
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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