A bag contains 6 green marbles, 8 yellow marbles, 9 white marbles. If one marble is drawn from the bag then replaced, what is the probability of drawing a green marble then a white marble? Round the answer to 4 decimal places. Enter your answer In a number guessing game. You ask a person to guess a number from one 1 to 10 . If the person makes a random guess, what is the probability their guess will be less than 7 ? Round the answer to 4 decimal places. Enter your answer A bag contains 8 black marbles, 9 white marbles, 6 yellow marbles. If one marble is drawn from the bag but not replaced, what is the probability of drawing a black marble then a yellow marble? Round the answer to 4 decimal places.

To find the probabilities, we first need to calculate the total number of marbles in each case. 1. For the bag containing 6 green, 8 yellow, and 9 white marbles, the total number of marbles is \(6 + 8 + 9 = 23\). The probability of drawing a green marble is \( \frac{6}{23} \), and since the marble is replaced, the probability of then drawing a white marble is \( \frac{9}{23} \). Thus, the combined probability of drawing a green marble followed by a white marble is: \[ P(\text{green then white}) = \frac{6}{23} \times \frac{9}{23} = \frac{54}{529} \approx 0.1021 \] 2. In the number guessing game from 1 to 10, the numbers less than 7 are 1, 2, 3, 4, 5, and 6. That gives us 6 favorable outcomes out of 10 possible guesses. Thus, the probability is: \[ P(\text{guess < 7}) = \frac{6}{10} = 0.6000 \] 3. For the second bag containing 8 black, 9 white, and 6 yellow marbles, the total number of marbles is \(8 + 9 + 6 = 23\). The probability of drawing a black marble first is \( \frac{8}{23} \). After drawing a black marble and not replacing it, there will be 22 marbles left. The number of yellow marbles remains 6. Therefore, the probability of then drawing a yellow marble is \( \frac{6}{22} = \frac{3}{11} \). The combined probability is: \[ P(\text{black then yellow}) = \frac{8}{23} \times \frac{6}{22} = \frac{48}{506} \approx 0.0948 \] In summary, the answers to the probabilities are: 1. 0.1021 2. 0.6000 3. 0.0948