Theoretical & Experimental Probability

What is an example of a real-life situation where you would use experimental probability?

• Conducting an experiment by flipping a coin 100 times and recording the number of heads and tails to determine the experimental probability of getting heads.

• Rolling a die once and recording the number that appears to find the theoretical probability of rolling a three.

• Choosing a random card from a deck and noting the suit to calculate the probability of drawing a heart.

• Observing the weather for a week and noting the number of sunny days to estimate the probability of sunny weather.

What is theoretical probability?

• The likelihood of an event occurring based on all possible outcomes in a perfect scenario, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

• The probability of an event based on past occurrences and historical data.

• The chance of an event happening in a real-world scenario without considering all possible outcomes.

• The likelihood of an event occurring based on subjective judgment rather than mathematical calculation.

What is the theoretical probability of drawing a green or red marble from a bag with 4 green, 3 red, 2 blue, and 1 yellow marble?

• 1/2

• 2/5

• 3/10

• 1/5

What is the theoretical probability of pulling a red marble from a bag containing 4 green, 3 red, 2 blue, and 1 yellow marble?

• P(Red) = 1/5

• P(Red) = 3/10

• P(Red) = 1/3

• P(Red) = 2/5

What is the theoretical probability of rolling an even number on a standard six-sided die?

• P(Even) = 1/3

• P(Even) = 1/4

• P(Even) = 1/2

• P(Even) = 2/3

What is the formula for calculating combinations in probability?

• Combinations = nCr = n! / (r!(n-r)!)

• Combinations = nCr = n! / (r!(n+r)!)

• Combinations = nCr = (n+r)! / (n!r!)

• Combinations = nCr = n! / (r!n!)

What is the probability of an impossible event?

• 0.5

• 1

• 0

• 0.25

If Robin has 5 pairs of shoes and 6 pairs of socks, how many combinations can she make?

• 20

• 25

• 30

• 35

How do you find the total number of combinations when choosing one item from multiple categories?

• Add the number of choices in each category together.

• Multiply the number of choices in each category together.

• Choose the largest category and use that number.

• Select one item from each category randomly.

What is the probability of an event that is certain to happen?

• 0

• 0.5

• 1

• 1.5