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Use probability to make decisions

Probability quantifies how likely an event is on a scale from 0 to 1, or equivalently from 0% to 100%, using equally likely outcomes, simple sample spaces, and experimental results represented as fractions, decimals, or percents. Learners compare probabilities to justify choices, distinguish greater likelihood from certainty, and recognize that a more probable outcome is not guaranteed; complex dependent events, expected value, and formal statistical decision analysis are beyond this scope.

Detailed Explanation: Use probability to make decisions

Probability tells how likely an event is.

  • 00 or 0%0\% means impossible.
  • 11 or 100%100\% means certain.
  • A probability between 00 and 11 means the event might happen, but it is not guaranteed.

For equally likely outcomes, use:

P(event)=number of favorable outcomestotal number of outcomesP(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}

To make a decision, find and compare the probabilities. Choose the option with the greater probability if you want the event to be more likely.

Example: You can choose one of two games. In each game, you win if you get blue.

  • Game A: Pick one marble from a bag with 33 blue marbles and 22 red marbles.
  • Game B: Spin a spinner divided into 88 equal sections. 55 sections are blue.

Which game should you choose to make winning more likely?

Step 1: Find the probability of winning Game A.

There are 3+2=53+2=5 marbles total, and 33 are blue.

P(win Game A)=35=0.6=60%P(\text{win Game A})=\frac{3}{5}=0.6=60\%

Step 2: Find the probability of winning Game B.

There are 88 equal sections, and 55 are blue.

P(win Game B)=58=0.625=62.5%P(\text{win Game B})=\frac{5}{8}=0.625=62.5\%

Step 3: Compare the probabilities.

62.5%>60%62.5\%>60\%

Game B has the greater probability of winning, so Game B is the better choice if you want to make winning more likely.

Remember: Game B is more likely to win, but winning is not certain. You could still land on a non-blue section.

Learn by doing: Use probability to make decisions

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Probability - Shapes, Two Sets of Two Shapes, Two Colors - Pick Two by Shape, To Percent


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