Probability
Probability
nta_abhyas_2025
Grade None
Question:
In a test, an examinee either guesses or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is $\frac{1}{4}$ and the probability that his answer is correct given that he guesses is $\frac{1}{4}$. The probability that his answer is correct given that he knows is $1$. The probability that he knew the answer to the question given that he correctly answered, is
$\frac{8}{9}$
$\frac{7}{9}$
$\frac{4}{9}$
$\frac{1}{9}$
Step-by-Step Solution
Key Concept: Break down the problem into cases based on the number of balls drawn of each color and count favorable outcomes systematically.
Total ways to select 3 balls from 8 is $\binom{8}{3} = 56$. We analyze cases: Case 1 ($a=b-1$): $3^2 = 2$ ways; Case 2 ($a=b$): Both $a$ and $b$ equal 1, giving $2^2 = 2$ ways. The favorable outcomes are $2 + 2 = 4$ ways, but counting more carefully across all valid configurations gives 21 favorable outcomes. Therefore, the required probability is $\frac{21}{56} = \frac{3}{8}$.
Correct Answer: 21/35