Question 1: Are There 3 Balls In A Hat, One With The Number

Question 1there Are 3 Balls In Ahat One With The Number 3 On It On

QUESTION 1 There are 3 balls in a hat; one with the number 3 on it, one with the number 4 on it, and one with the number 7 on it. You pick a ball from the hat at random and then you flip a coin. Using a tree diagram, obtain the sample space for the experiment. List the elements that make up the sample space.

Paper For Above instruction

In this experiment, the process involves two stages: selecting a ball from a hat containing three distinct balls and flipping a coin. To accurately represent all possible outcomes, a tree diagram helps visualize the sequential choices. First, each ball choice is considered followed by the coin flip outcome, either heads (H) or tails (T).

The sample space includes all possible combinations resulting from these two steps. The possible outcomes are:

  • Number 3 with coin heads (3 H)
  • Number 3 with coin tails (3 T)
  • Number 4 with coin heads (4 H)
  • Number 4 with coin tails (4 T)
  • Number 7 with coin heads (7 H)
  • Number 7 with coin tails (7 T)

Thus, the sample space is the set {3 H, 3 T, 4 H, 4 T, 7 H, 7 T}. Each element represents a unique outcome of the combined process of selecting a ball and flipping the coin. This comprehensive list accounts for all possible outcomes, confirming the total sample size of six possible outcomes.

References

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