How to Solve Theoretical Probability?

How to Solve Theoretical Probability?

How to find theoretical probability?

Step 1: Identify the number of favorable outcomes. Since there are (20) lottery tickets, (20) will be the desired number of results.

Tutor-style math help

Solve Theoretical Probability: what to notice and how to work it

Probability skill
Probability compares favorable outcomes with possible outcomes. The rule changes when events are independent, dependent, mutually exclusive, or conditional.

What to notice first

Define the event before calculating. A clear sample space prevents most probability mistakes.

Common student mistake

Do not multiply probabilities until you know the events are independent or the second probability is conditional.

Key formulas and cues

(P(A)=frac{text{favorable}}{text{total}})
(P(Atext{ and }B)=P(A)P(B)text{ if independent})
(P(A|B)=frac{P(Acap B)}{P(B)})
HTHHHTTHTT

A reliable path

  1. List outcomesName the possible results or count them carefully.
  2. Choose the ruleUse addition, multiplication, or conditional probability based on the wording.
  3. Check the rangeA probability must be between 0 and 1.

Worked examples

Simple probability

Example: Roll an even number on a fair die
  1. Even outcomes are 2, 4, and 6.
  2. There are 3 favorable outcomes out of 6.
  3. Reduce the fraction.
Answer: (frac12)

Independent events

Example: Flip two heads in a row
  1. P(heads) = 1/2 for each flip.
  2. The flips are independent.
  3. Multiply 1/2 by 1/2.
Answer: (frac14)
Open pop-up practice
Try one before moving on
Try: A fair coin is flipped once. What is P(tails)?
Answer: (frac12).
Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

Step 2: Determine the total possible outcomes. Since a total of (600) tickets were sold in this way, (600) will be the total number of possible results.

Step 3: Divide the value from step (1) by step (2) to calculate the theoretical probability. Therefore, (frac{20}{600}=0.03). This indicates that the probability of a person winning a lottery prize is (0.03).

Theoretical Probability, Example 1:

Find the probability of getting (2) on a fair die.

Solution:

The possible outcomes of rolling a die are (1, 2, 3, 4, 5, 6), so the total number of outcomes (=6). As we want to calculate the probability of getting only (2), therefore, the number of desired outcomes (= 1).

(pleft(2right)=frac{1}{6}=0.16)

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