How would you decide the probability of each of the following? Choose A equally likely outcomes, or B experimental evidence . Write A and B on the answer line.
Questions: First: A die is thrown. What proportion of times is 6 scored?
Second: One hundred drawing-pins are dropped onto the floor .What proportion land point up?
Third: Anna and karen compete in some cycle races. what proportion of the time will Anna win?
Q1 — 1/6
Q2 — DK, more data needed, but would guess very unlikely
Q3 — DK, more data needed, what was their past performance?
To determine the probability of each of the scenarios you mentioned, we can use two main approaches: A) equally likely outcomes or B) experimental evidence.
1. First question: A die is thrown. What proportion of times is 6 scored?
A) Equally likely outcomes: Assuming the die is fair, meaning all six sides are equally likely to be rolled, there are six possible outcomes (numbers 1 to 6). Therefore, the probability of scoring a 6 is 1 out of 6, which can be written as 1/6.
B) Experimental evidence: To determine the actual probability of scoring a 6, you can conduct an experiment by rolling the die a large number of times and recording the number of times a 6 is observed. By dividing the number of 6s rolled by the total number of rolls, you can estimate the experimental probability. The more rolls you perform, the closer your estimate will be to the true probability of 1/6.
2. Second question: One hundred drawing-pins are dropped onto the floor. What proportion land point up?
A) Equally likely outcomes: Assuming each drawing-pin has an equal chance of landing point up or down, there are two equally likely outcomes for each individual drawing-pin. Therefore, the probability of a pin landing point up is 1 out of 2, which can be written as 1/2.
B) Experimental evidence: One way to determine the actual probability experimentally is by dropping the drawing-pins a large number of times and counting the number of pins that land point up. Again, dividing the number of pins that landed point up by the total number of drops will provide an estimate of the experimental probability.
3. Third question: Anna and Karen compete in some cycle races. What proportion of the time will Anna win?
A) Equally likely outcomes: If Anna and Karen are equally skilled, assuming there are no other factors that may influence the outcome, then the probability of Anna winning is 1 out of 2, which can be written as 1/2. This is based on the assumption that each outcome (Anna winning or Karen winning) is equally likely.
B) Experimental evidence: To determine the actual probability, you can analyze their previous race records. By calculating the proportion of races Anna has won out of the total races they have competed, you can estimate the experimental probability of Anna winning. This approach relies on historical data and may vary depending on their respective skills, conditions, and other factors.