Probability
Probability
nta_abhyas_2025
Grade 12
Question:
NTA Test 15 (Numerical)
A bag contains a mixed lot of red and blue balls. If two balls are drawn at random, the probability of drawing two blue balls and the probability of drawing one ball of each colour is six times the probability of drawing two blue balls. Then, the total number of red and blue balls in the bag is
Step-by-Step Solution
Key Concept: Use the complement rule and binomial probability to set up an inequality and solve for the parameter $n$.
Given that $P(2) + P(3) \geq 0.96$, we need to find $n$ such that $1 - P(0) - P(1) \geq 0.96$, which means $P(0) + P(1) \leq 0.04$. For a binomial distribution, $P(0) + P(1) = (0.04)^n + n(0.04)^{n-1}(0.96) \leq 0.04$. Testing values: $(0.04)^2 + 2(0.04)(0.96) = 0.0016 + 0.0768 > 0.04$; but $4^2 \geq (n+1)100$ gives us $n = 8$. Verification: $2^{20} > 900$ implies $n = 8$.
Correct Answer: 8