Questions: 14) What is the probability of rolling a 3 on a 6 -sided number cube and then NOT rolling a 3 on a 6 sided number cube?

Solution Steps

To find the probability of rolling a 3 on a 6-sided number cube and then not rolling a 3 on a 6-sided number cube, we need to calculate the probability of each event separately and then multiply them together. The probability of rolling a 3 on the first roll is 1/6, and the probability of not rolling a 3 on the second roll is 5/6.

The probability of rolling a 3 on a 6-sided number cube is given by: \[ P(\text{roll 3}) = \frac{1}{6} \approx 0.1667 \]

The probability of not rolling a 3 on a 6-sided number cube is given by: \[ P(\text{not roll 3}) = \frac{5}{6} \approx 0.8333 \]

The combined probability of rolling a 3 on the first roll and not rolling a 3 on the second roll is the product of the two individual probabilities: \[ P(\text{roll 3 and not roll 3}) = P(\text{roll 3}) \times P(\text{not roll 3}) = 0.1667 \times 0.8333 \approx 0.1389 \]

Final Answer