Understanding Probability - Pre Algebra

1. What is the relative frequency of an event, and how does it relate to probability?

   The number of times the event occurs divided by the number of trials. Over many trials it tends to approach the probability.

2. A coin is flipped 100 times and lands heads 47 times. What is the relative frequency of heads?

   $0.47$. $\frac{47}{100} = 0.47$.

3. A fair coin flipped 10 times lands heads 7 times. Why does this not mean the probability of heads is $0.7$?

   Short runs vary a lot. The relative frequency of heads approaches $0.5$ only over many flips.

4. What is theoretical probability based on?

   Reasoning about the equally likely outcomes of a situation, rather than on results from actual trials.

5. Which event is more likely: one with probability $0.7$ or one with probability $\frac{3}{5}$?

   The event with probability $0.7$. $\frac{3}{5} = 0.6$, which is less than $0.7$.

6. What does a probability of $\frac{1}{2}$ mean?

   The event is equally likely to occur or not occur.

7. What does a probability of 1 mean?

   The event is certain; it will always occur.

8. Which of these cannot be a probability: $0.9$, $\frac{5}{4}$ or $0$?

   $\frac{5}{4}$. It is greater than 1, and no probability can exceed 1.

9. An event has probability $0.2$. About how many times should it occur in 50 trials?

   About 10 times. $0.2 \times 50 = 10$.

10. What does a probability of 0 mean?

    The event is impossible; it will never occur.

11. What range of values can a probability have?

    From 0 to 1, inclusive. It can also be written as a percent from $0\%$ to $100\%$.

12. How would you describe the likelihood of an event with probability $0.95$?

    Very likely. Its probability is close to 1, so in the long run it happens in about 95 of every 100 trials.

Study these flashcards