Question

a bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. two marbles are drawn from the bag.

which expression represents the probability that one of the marbles is red and the other is blue?

option 1: \frac{(_{10}p_1)(_{20}p_1)}{_{50}p_2}
option 2: \frac{_{30}p_2}{_{50}p_2}
option 3: \frac{(_{10}c_1)(_{20}c_1)}{_{50}c_2}
option 4: \frac{_{30}c_2}{_{50}c_2}

Explanation:

Calculate total marbles and sample space

$$
LATEXBLOCK0
$$

Calculate favorable outcomes

$$
LATEXBLOCK1
$$

Formulate probability expression

$$ P(\text{1 red and 1 blue}) = \frac{({}_{10}\text{C}_{1})({}_{20}\text{C}_{1})}{{}_{50}\text{C}_{2}} $$

Answer:

• (A) \frac{({}_{10}\text{P}_{1})({}_{20}\text{P}_{1})}{{}_{50}\text{P}_{2}}
• (B) \frac{{}_{30}\text{P}_{2}}{{}_{50}\text{P}_{2}}
• (C) \frac{({}_{10}\text{C}_{1})({}_{20}\text{C}_{1})}{{}_{50}\text{C}_{2}} (Correct answer)
• (D) \frac{{}_{30}\text{C}_{2}}{{}_{50}\text{C}_{2}}