Question

A bag contains five green marbles and seven yellow marbles. You randomly select three marbles. What is the probability that all three marbles are green when (a) you replace each marble before selecting the next marble, and (b) you do not replace each marble before selecting the next marble? Write each probability as a decimal rounded to the nearest thousandth. Then compare the probabilities, i a. When you replace each marble before selecting the next marble, the probability is 0.25 b. When you do not replace each marble before selecting the next marble, the probability is 0.08 To the nearest tenth, you are about 3.1 times more likely to select three green marbles when you replace each marble before you select the < next marble.

Answer 1

The probability of selecting three green marbles from the bag is 0.115 when each marble is replaced, and 0.091 when each marble is not replaced. We are about 3.1 times more likely to select three green marbles when each marble is replaced.

Step-by-step explanation:

In this problem, we are given a bag containing five green marbles and seven yellow marbles. We are asked to find the probability of selecting three green marbles for two scenarios: when we replace each marble before selecting the next one, and when we do not replace each marble before selecting the next one.

When each marble is replaced, the probability of selecting a green marble is 5/12. Since each selection is independent, we multiply the probabilities for each selection: (5/12) * (5/12) * (5/12) = 0.115, which rounds to 0.115.

When each marble is not replaced, the probability of selecting a green marble on the first selection is 5/12. However, for the second selection, there are now only 4 green marbles left out of a total of 11 marbles. So the probability for the second selection is 4/11. Similarly, for the third selection, there are 3 green marbles left out of 10 marbles. So the probability for the third selection is 3/10. Again, we multiply the probabilities for each selection: (5/12) * (4/11) * (3/10) = 0.091, which rounds to 0.091.

Therefore, to the nearest tenth, we are about 3.1 times more likely to select three green marbles when we replace each marble before selecting the next one.