a bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. two…

a bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. two marbles are chosen from the bag. what expression would give the probability that one marble is yellow and the other marble is red?\n\n$p(y\\text{ and }r)=\\frac{(_{8}p_{1})(_{5}p_{1})}{_{25}p_{2}}$\n\n$p(y\\text{ and }r)=\\frac{(_{8}c_{1})(_{5}c_{1})}{_{25}c_{2}}$\n\n$p(y\\text{ and }r)=\\frac{(_{1}c_{8})(_{1}c_{5})}{_{2}c_{25}}$\n\n$p(y\\text{ and }r)=\\frac{(_{1}p_{8})(_{1}p_{5})}{_{2}p_{25}}$\n

a bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. two marbles are chosen from the bag. what expression would give the probability that one marble is yellow and the other marble is red?\n\n$p(y\\text{ and }r)=\\frac{(_{8}p_{1})(_{5}p_{1})}{_{25}p_{2}}$\n\n$p(y\\text{ and }r)=\\frac{(_{8}c_{1})(_{5}c_{1})}{_{25}c_{2}}$\n\n$p(y\\text{ and }r)=\\frac{(_{1}c_{8})(_{1}c_{5})}{_{2}c_{25}}$\n\n$p(y\\text{ and }r)=\\frac{(_{1}p_{8})(_{1}p_{5})}{_{2}p_{25}}$\n

Answer

Explanation:

Step1: Calculate total number of marbles

Total marbles = 8 (yellow) + 9 (green) + 3 (purple) + 5 (red) = 25 marbles.

Step2: Use combination formula for probability

The probability of choosing one yellow and one red marble when choosing 2 marbles out of 25 is given by the number of ways to choose 1 yellow out of 8 and 1 red out of 5, divided by the number of ways to choose 2 marbles out of 25. The number of ways to choose (r) items from (n) items is (C(n,r)=\frac{n!}{r!(n - r)!}). The number of ways to choose 1 yellow out of 8 is ({8}C{1}), 1 red out of 5 is ({5}C{1}), and 2 marbles out of 25 is ({25}C{2}). So (P(Y\text{ and }R)=\frac{({8}C{1})({5}C{1})}{{25}C{2}}).

Answer:

(P(Y\text{ and }R)=\frac{({8}C{1})({5}C{1})}{{25}C{2}}) (the second option)