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Probability of Sums and Three Independent Events in Games

This lesson explores the concepts of probability through engaging examples involving spinners and canes. In Example 2, students will find the probability that the sum of values from two spinners is at least 4, using a table of sums to visualize outcomes. Example 3 introduces three independent events with canes tossed to discover the probability that all land the same side up. These examples help students understand how to calculate probabilities using different methods, such as tables and tree diagrams.

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Probability of Sums and Three Independent Events in Games

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  1. EXAMPLE 2 Probability of a Sum

  2. EXAMPLE 2 Probability of a Sum The spinners at the right are each divided into equal parts. You spin the spinners. Find the probability that the sum is at least 4.

  3. EXAMPLE 2 Probability of a Sum The spinners at the right are each divided into equal parts. You spin the spinners. Find the probability that the sum is at least 4. SOLUTION You can use a table of sums to list All the possible outcomes

  4. EXAMPLE 2 Probability of a Sum The spinners at the right are each divided into equal parts. You spin the spinners. Find the probability that the sum is at least 4. SOLUTION You can use a table of sums to list All the possible outcomes

  5. EXAMPLE 2 Probability of a Sum The spinners at the right are each divided into equal parts. You spin the spinners. Find the probability that the sum is at least 4. SOLUTION You can use a table of sums to list All the possible outcomes 9 of the 12 sums are at least 4.

  6. EXAMPLE 2 Probability of a Sum The spinners at the right are each divided into equal parts. You spin the spinners. Find the probability that the sum is at least 4. SOLUTION You can use a table of sums to list All the possible outcomes 9 of the 12 sums are at least 4. ANSWER The probability that the sum is at least 4 is . 3 9 = 4 12

  7. EXAMPLE 3 Three Independent Events

  8. EXAMPLE 3 Three Independent Events Games You are playing a game in which 3 canes are tossed. One side of each cane is flat, and the other side is round. Find the probability that all 3 canes land the same side up.

  9. EXAMPLE 3 Three Independent Events Games You are playing a game in which 3 canes are tossed. One side of each cane is flat, and the other side is round. Find the probability that all 3 canes land the same side up. SOLUTION You can use a tree diagram to find all the possible outcomes.

  10. EXAMPLE 3 Three Independent Events

  11. EXAMPLE 3 Three Independent Events The probability that all 3 canes land the same side up is . ANSWER 2 1 = 8 4

  12. for Examples 2 and 3 GUIDED PRACTICE Find the probability of the event. 4. The sum in Example 2 is at most 4. ANSWER 5 of the 12 sums are at most 4. The probability that the sum is at most 4 is . 5 12

  13. R R R R R F R F R R F F F R R F R F F F R F F F for Examples 2 and 3 GUIDED PRACTICE 5. Exactly one cane in Example 3 lands flat side up. ANSWER 3 . Out of 8, 3 canes lands flat side up once. So solution is 8

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