a six - sided number cube is rolled and the proportion of 3s is calculated. the graph shows the long - run…

a six - sided number cube is rolled and the proportion of 3s is calculated. the graph shows the long - run relative frequency of 100 rolls of this die. which conclusion can be drawn from this graph? there is a 20% chance of rolling a 3 with this die. the long - run frequency of rolling a 3 appears to be about 0.17. because the probabilities on the left part of the graph fluctuate so much, we cannot conclude that this is a fair number cube. this number cube must be fair because each outcome of rolling a 1, 2, 3, 4, 5, or 6 has the same probability of occurring. proportion of 3s probability 0.2 0.15 0.1 0.05 0 20 40 60 80 100 frequency

a six - sided number cube is rolled and the proportion of 3s is calculated. the graph shows the long - run relative frequency of 100 rolls of this die. which conclusion can be drawn from this graph? there is a 20% chance of rolling a 3 with this die. the long - run frequency of rolling a 3 appears to be about 0.17. because the probabilities on the left part of the graph fluctuate so much, we cannot conclude that this is a fair number cube. this number cube must be fair because each outcome of rolling a 1, 2, 3, 4, 5, or 6 has the same probability of occurring. proportion of 3s probability 0.2 0.15 0.1 0.05 0 20 40 60 80 100 frequency

Answer

Explanation:

Step1: Analyze long - run frequency

In the long - run relative frequency graph, as the number of rolls increases, the proportion of 3s stabilizes around 0.17.

Step2: Evaluate each option

  • Option 1: There is no indication of a 20% (0.2) chance from the graph.
  • Option 2: The graph shows the long - run frequency of rolling a 3 appears to be about 0.17, which is consistent with the graph's trend.
  • Option 3: Just because the early part of the graph fluctuates does not mean we cannot conclude about fairness. The long - run behavior matters more.
  • Option 4: We cannot conclude fairness just from this graph of the proportion of 3s.

Answer:

The long - run frequency of rolling a 3 appears to be about 0.17.