Q: Which formula is used to calculate the theoretical probability of an event $E$?

$P(E) = \frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}$

Q: A cup is tossed 50 times and lands upright 15 times. If you want to estimate the probability of landing upright in the future, which formula should you use?

$P(E) = \frac{\text{number of times event occurs}}{\text{number of trials}}$

Question 1

A plastic cup is tossed, and it can land either on its side or upright. If the cup is equally likely to land in either position, what is the theoretical probability that it lands upright?

Accepted Answer

$\frac{1}{2}$

Question 2

Which formula is used to calculate the theoretical probability of an event $E$?

Accepted Answer

$P(E) = \frac{	ext{number of favorable outcomes}}{	ext{number of possible outcomes}}$

Question 3

Suppose you toss a plastic cup 100 times and it lands upright 27 times. What is the empirical probability that the cup lands upright?

Accepted Answer

$\frac{27}{100}$

Question 4

If an event is certain to happen, what is its probability?

Accepted Answer

$1$

Question 5

A student claims that the probability of a plastic cup landing on its side is $0.7$ based on 70 out of 100 tosses. What type of probability is this?

Accepted Answer

Empirical probability

Question 6

Which of the following best describes the difference between theoretical and empirical probability?

Accepted Answer

Theoretical probability is based on reasoning, while empirical probability is based on actual experiments.

Question 7

If a plastic cup is tossed and the probability of landing upright is $0.3$, what is the probability it lands on its side?

Accepted Answer

$0.7$

Question 8

A cup is tossed 50 times and lands upright 15 times. If you want to estimate the probability of landing upright in the future, which formula should you use?

Accepted Answer

$P(E) = \frac{	ext{number of times event occurs}}{	ext{number of trials}}$

Question 9

If the probability of an event is $0$, what does this mean?

Accepted Answer

The event is impossible.

Question 10

A plastic cup is tossed and can land in three ways: upright, on its side, or upside down. If each outcome is equally likely, what is the probability it lands upside down?

Accepted Answer

$\frac{1}{3}$

Question 11

In a probability experiment, which of the following is an example of a trial?

Accepted Answer

Tossing a plastic cup once

Question 12

If you toss a cup 200 times and it lands upright 60 times, what is the empirical probability of landing upright?

Accepted Answer

$\frac{60}{200}$

Question 13

Which of the following statements is true about probability values?

Accepted Answer

Probability values are always between $0$ and $1$, inclusive.

Question 14

A cup is tossed and the probability of landing upright is $0.25$. If you toss the cup 80 times, about how many times would you expect it to land upright?

Accepted Answer

$20$

Question 15

If the probability of a cup landing upright is $0.4$ and you toss the cup 10 times, what is the expected number of times it will land upright?

Accepted Answer

$4$

Probability Concepts in College Algebra

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