Probability
Definition
Probability is the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
Analogy
Think of probability as flipping a fair coin. The probability of getting heads is 0.5 because there are two equally likely outcomes (heads or tails), and one favorable outcome (getting heads).
Related terms
Random Variable: A random variable is a numerical value that represents the outcome of a random experiment.
Sample Space: The sample space is the set of all possible outcomes in a random experiment.
Conditional Probability: Conditional probability measures the likelihood of an event happening given that another event has already occurred.
"Probability" appears in:
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Practice Questions (20+)
How can the probability of a Type II error be reduced?
Which of the following increases the probability of making a Type II error?
When testing a statistical claim or estimating a population proportion, what type of curve is often used to calculate the probability in the sampling distribution?
What is the probability of getting exactly 3 successes in 5 independent trials, given a probability of success of 0.4?
What is the probability of getting exactly 2 successes in 6 independent trials, given a probability of failure of 0.1?
What is the probability of getting at most 2 successes in 4 independent trials, given a probability of success of 0.6?
What is the probability of getting more than 3 successes in 6 independent trials, given a probability of success of 0.8?
A student wants to conduct a simulation to estimate the probability of rolling a sum of 8 with two six-sided dice. Which of the following is the most appropriate method for conducting the simulation?
A simulation is conducted to estimate the probability of drawing a red card from a well-shuffled deck of playing cards. The simulation is repeated 1,000 times, and a red card is drawn 700 times. What can be concluded about the estimated probability based on this simulation?
A simulation is conducted to estimate the probability of rolling a number greater than 4 on a six-sided die. The die is rolled 500 times in the simulation, and a number greater than 4 is rolled 350 times. What is the estimated probability based on this simulation?
A statistics professor wants to estimate the probability of drawing a heart from a standard deck of 52 playing cards. The professor conducts a simulation by randomly drawing cards from the deck 1,000 times and records the number of hearts drawn. Which of the following would be the most appropriate method for estimating the probability?
A simulation is conducted to estimate the probability of rolling a number less than or equal to 2 on a fair six-sided die. The die is rolled 200 times in the simulation, and a number less than or equal to 2 is rolled 50 times. What is the estimated probability based on this simulation?
A student conducts a simulation to estimate the probability of getting heads when flipping a fair coin. The coin is flipped 500 times in the simulation, and heads is observed 240 times. What is the estimated probability based on this simulation?
If a sample space has 10 equally likely outcomes, and event B consists of 4 of those outcomes, what is the probability of event B occurring?
In a deck of playing cards, what is the probability of drawing a spade and then drawing an ace (without replacement)?
In a bag containing 5 red balls, 3 blue balls, and 2 green balls, what is the probability of randomly selecting a blue ball and then selecting a green ball (without replacement)?
In a class, 45% of the girls are in a sport and 43% of the boys play a sport. Suppose that 48% of the class are girls. If we choose a person from the class at random, what is the probability they are a girl given that they play sports?
Events A and B are independent. The probability of event A happening is 0.7 and the probability of both events occurring is 0.56. What is the probability of event B?
If the probability of event A occurring is 0.4 and the probability of event A occurring given that event B occurs is 0.6, are event A and event B independent?
What formula can you use to calculate the probability of a discrete random variable taking on a particular value?
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