Probability Concepts and Calculations

Probability Concepts

• Probability measures the likelihood of an event occurring. It's expressed as a fraction, decimal, or percentage, ranging from 0 (impossible) to 1 (certain).

Determining Probability

• Impossible: An event that cannot occur (probability = 0).
• Unlikely: An event that is not expected to occur frequently (probability < 0.5 ).
• Even: An event that is equally likely to occur or not occur (probability = 0.5).
• Likely: An event that is expected to occur frequently (probability > 0.5).
• Certain: An event that is guaranteed to occur (probability = 1).

Calculating Probability (from examples)

• Tossing a fair coin, landing on tails: Probability = 1/2
• The sun shining in South Carolina this summer: Probability is variable (dependent on weather).
• Living to 500 years old: Probability extremely low/ practically impossible.

Probability of Events with Cards:

• A 46-card deck is unspecified (needs details for specific calculations).
• P(rectangle): Requires the number of rectangles in the shown deck.
• P(not a star): Requires the number of non-stars to calculate (likewise for stars).

Probability of Events with Marbles:

• Ilana picks from a bag with 4 Blue, 3 Red, 2 Yellow, and 5 Green marbles.
• Probability of picking a marble that is NOT red = (4 + 2 + 5) / (4 + 3 + 2 + 5) = 11/14

Probability in a Card Game(Bridge):

• Kevin has 5 spades, 3 hearts, 4 diamonds, and 1 club (total of 13 cards)
• Probability examples for these cards are not provided

Probabilities of a Spinner

• 8-section spinner numbered 1-8.
• Probability of spinning an 8 = 1/8

Overall Probability Calculations

• The sum of probabilities for all possible outcomes in an event is always 1.
• This is true for the spinner's 1-8 options (sum of probabilities = 1).
• Probability of spinning a specific number (e.g., number 2) needs spinner sections for calculation.

Experimental vs Theoretical Probability:

• Experimental probability is determined by observing an event happen in the real world (like spinning a spinner or rolling a die)
• Theoretical probability is worked out based on a set of possibilities and is derived from mathematical reasoning (like in calculating the probabilities of rolling a dice or cards).

Rolling a Number Cube:

• Experimental probability of rolling an even number (needs data like frequency of each roll).
• Theoretical probability of rolling an even number (1/2).
• Experimental probability of rolling a 2 (needs data from the experiment).
• Theoretical probability of rolling a 2 (1/6)

Using a Paper Clip as an Arrow:

• Experimental and theoretical probabilities are needed for finding probabilities of events like "spinning a number greater than 1" and "spinning a 1 or a 2." Incomplete data in the provided text for calculations.

Overall Probabilities

• Total probability for a set of outcomes (total probability of spinning either 1, 2, 3, or 4 on the spinner) is calculated by adding the probabilities of those individual outcomes and should equal 1.

Likelihood to spin an 8 on a spinner

• How likely it is to spin an 8 on this 8-section spinner (needs spinner details; probability is 1/8).