Question 1
We want to choose a white marble, then a black marble.
- The probability of choosing a white marble is 9/(9+7+8)=9/24.
- The probability of choosing a black marble is 8/(9+7+8)=8/24.
Multiplying these probabilities, we get (9/24)(8/24) = 1/8.
Question 2
- For the guess to be less than 6, they have to choose 1, 2, 3, 4, or 5.
Thus, the probability is 5/10 = 1/2.
Question 3
- The probability of choosing a yellow marble is 7/(7+8+9)=7/24.
- The probability of choosing a green marble after is 9/(6+8+9)=9/23. [Note that the 7 yellow marbles is now 6 since we are assuming a yellow marble was drawn beforehand]
Multiplying these probabilities, we get (7/24)(9/23) = 21/184.
