NTA Test 18 (Single Choice)
A small pack of cards consists of 5 green cards, 4 blue cards and 3 black cards. The pack is shuffled through and first three cards are turned face up. The probability that there is exactly one card of each colour is
Step-by-Step Solution
Key Concept: Use the relationships between probabilities of different ball-drawing outcomes to set up equations for the number of red and blue balls.
Let $a$ be the number of red balls and $b$ be the number of blue balls. We are given that $p_1 = 5p_2$ and $p_2 = 6p_3$, where $p_1$ is the probability of drawing two blue balls, $p_2$ is the probability of drawing one red and one blue ball, and $p_3$ is the probability of drawing two red balls. From the condition $p_1 = 5p_2$ and $p_2 = 6p_3$, we get $a(a-1) = 9b(b-1)$ and $2ab = 5ab(a-1)$. Solving these equations yields $a = 4$ and $b = 3$. Therefore, the total number of balls is $a + b = 9$.
Correct Answer: 9