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

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?\n$\frac{_{30}p_{2}}{_{50}p_{2}}$\n$\frac{_{30}c_{2}}{_{50}c_{2}}$\n$\frac{(_{10}c_{1})(_{20}c_{1})}{_{50}c_{2}}$\n$\frac{(_{10}p_{1})(_{20}p_{1})}{_{50}p_{2}}$\n

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?\n$\frac{_{30}p_{2}}{_{50}p_{2}}$\n$\frac{_{30}c_{2}}{_{50}c_{2}}$\n$\frac{(_{10}c_{1})(_{20}c_{1})}{_{50}c_{2}}$\n$\frac{(_{10}p_{1})(_{20}p_{1})}{_{50}p_{2}}$\n

Answer

Explanation:

Step1: Calculate total number of marbles

The total number of marbles is (10 + 15+5 + 20=50).

Step2: Determine the number of ways to choose one - red and one - blue marble

The number of ways to choose 1 red marble out of 10 is ({10}C{1}), and the number of ways to choose 1 blue marble out of 20 is ({20}C{1}). By the multiplication principle, the number of ways to choose one red and one blue marble is (({10}C{1})({20}C{1})).

Step3: Calculate the total number of ways to choose 2 marbles out of 50

The total number of ways to choose 2 marbles out of 50 is ({50}C{2}).

Step4: Find the probability

The probability that one of the marbles is red and the other is blue is given by the ratio of the number of favorable outcomes to the total number of outcomes, which is (\frac{({10}C{1})({20}C{1})}{{50}C{2}}).

Answer:

(\frac{({10}C{1})({20}C{1})}{{50}C{2}})