Question

Irving has a bag containing seven yellow marbles, six siver marbles and four red marbles. Irving draws marbles at random from the bag, ten times with replacement. What is the probability that he will draw exactly five yellow marbles and exactly two silver marbles among the ten marbles drawn?

Answer 1

To find the probability of drawing exactly five yellow marbles and exactly two silver marbles among the ten marbles drawn, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

Step-by-step explanation:

To find the probability of drawing exactly five yellow marbles and exactly two silver marbles among the ten marbles drawn, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

There are 7 yellow marbles, 6 silver marbles, and 4 red marbles in the bag, so the total number of marbles is 17.

The number of ways to draw 5 yellow marbles from 10 draws is 10C5.

The number of ways to draw 2 silver marbles from the remaining 5 draws is 5C2.

The number of ways to draw the remaining marbles (from the remaining 3 draws) is 3C3.

Therefore, the probability is (10C5)(5C2)(3C3) / 17^10.

Calculating the value will give us the exact probability.