Final answer:
To calculate the probability of rolling exactly one six with a biased die with a 1/5 probability of six, consider two scenarios: a six then not a six, and not a six then a six. Each scenario has a probability of 4/25, making the total probability 8/25.
Step-by-step explanation:
The question is about calculating the probability of rolling exactly one six with a biased die when the given probability of rolling a six is 1/5. A tree diagram would depict two possibilities for each roll: rolling a six (with a probability of 1/5) or not rolling a six (with a complementary probability of 4/5).
To find the probability of rolling exactly one six in two rolls, we look at two distinct events: rolling a six on the first roll and not on the second (6-Not 6), and not rolling a six on the first roll but rolling it on the second (Not 6-6). The probabilities for these chains of events are calculated as:
- For the first scenario (6-Not 6): (1/5) * (4/5) = 4/25.
- For the second scenario (Not 6-6): (4/5) * (1/5) = 4/25.
The total probability of exactly one six in two rolls is the sum of these individual probabilities: 4/25 + 4/25 = 8/25.