Solution: Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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Now we will solve this DS question using the Variable Approach.
TIP 1: When the value from condition (1) and the value from condition (2) are the same, D would be the most likely answer.
Let’s apply the 3 steps suggested previously.
Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.
Let us assign variable: Males (m) and Females (f)
Total number of departments: 19 => m + f = 19
Head of departments: Males (13) and Females (6).
We have to find the probability that the head of the department selected will be a female who is pursuing Ph. D. program.
Follow the second and the third step: From the original condition, we have 2 variables (m and f) and 1 Equation ( m + f = 19). To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately.
Condition (1) tells us that among the females, three are pursuing Ph. D. program.
Total females: 6 and ‘3’ out of ‘6’ are pursuing a Ph.D.
=> Required Probability: \(\frac{3}{19}\)
The answer is unique, condition (1) alone is sufficient according to Common Mistake Type 2 which states that the number of answers must be only one.
Condition (2) tells us that among the females, three are not pursuing Ph. D. program.
Total females: 6 and ‘3’ out of ‘6’ are not pursuing a Ph.D. This means ‘3’ out of ‘6’ are pursuing a Ph.D.
=> Required Probability: \(\frac{3}{19}\)
The answer is unique, condition (2) alone is sufficient according to Common Mistake Type 2 which states that the number of answers must be only one.
EACH condition ALONE is sufficient.
So, D is the correct answer.
Answer: D
Also, according to Tip 1, if both the conditions give the same value, a=1 here, the most probable answer is D. It is about 95% likely that D would be the answer when the value of the condition (1) is equal to the value of the condition (2).
The answer is D because (1) = (2).
Answer: D
