Question

probability and statistics
a bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. two marbles are drawn from the
which expression represents the probability that one of the marbles is red and the other is blue?

Explanation:

Step1: Calculate total number of marbles

Total marbles \(n = 10 + 15+5 + 20=50\)

Step2: Use combination formula for probability

Probability of choosing one red and one blue marble:
Number of ways to choose 1 red out of 10: \(_{10}C_{1}=\frac{10!}{1!(10 - 1)!}=10\)
Number of ways to choose 1 blue out of 20: \(_{20}C_{1}=\frac{20!}{1!(20 - 1)!}=20\)
Number of ways to choose 2 marbles out of 50: \(_{50}C_{2}=\frac{50!}{2!(50 - 2)!}=\frac{50\times49}{2\times 1}\)
Probability \(P=\frac{(_{10}C_{1})(_{20}C_{1})}{_{50}C_{2}}\)

Answer:

\(\frac{(_{10}C_{1})(_{20}C_{1})}{_{50}C_{2}}\) (the fourth option)