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.

Step2: Determine number of ways to choose 1 yellow marble

There are 8 yellow marbles, and the number of ways to choose 1 yellow marble out of 8 is given by the combination formula ({8}C{1}=\frac{8!}{1!(8 - 1)!}=8).

Step3: Determine number of ways to choose 1 red marble

There are 5 red marbles, and the number of ways to choose 1 red marble out of 5 is ({5}C{1}=\frac{5!}{1!(5 - 1)!}=5).

Step4: Determine number of ways to choose 2 marbles out of 25

The number of ways to choose 2 marbles out of 25 is ({25}C{2}=\frac{25!}{2!(25 - 2)!}=\frac{25\times24}{2\times 1}=300).

Step5: Calculate the probability

The probability that one marble is yellow and the other is red is the product of the number of ways to choose 1 - yellow and 1 - red marble divided by the number of ways to choose 2 marbles out of 25. 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 in the multiple - choice list)