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Galina spins a spinner with three equally sized colored sections: red, green, and purple. She also rolls a number cube. Which event below has the highest likelihood of occurring?(1 point) Responses The spinner lands on red, and the number cube lands on an even number. The spinner lands on red, and the number cube lands on an even number. The spinner lands on either purple or red, and the number cube lands on 3. The spinner lands on either purple or red, and the number cube lands on 3. The spinner lands on either green or red, and the number cube lands on 6. The spinner lands on either green or red, and the number cube lands on 6. The spinner lands on red, and the number cube lands on 6. pick one'

1 answer

To determine which event has the highest likelihood, let’s analyze the probabilities of each event:

  1. The spinner lands on red, and the number cube lands on an even number.

    • Probability of spinner landing on red = 1/3
    • Even numbers on a number cube (2, 4, 6) = 3 possible outcomes
    • Probability of rolling an even number = 3/6 = 1/2
    • Combined Probability = (1/3) * (1/2) = 1/6

  2. The spinner lands on either purple or red, and the number cube lands on 3.

    • Probability of spinner landing on purple or red = 2/3
    • Probability of rolling a 3 = 1/6
    • Combined Probability = (2/3) * (1/6) = 2/18 = 1/9

  3. The spinner lands on either green or red, and the number cube lands on 6.

    • Probability of spinner landing on green or red = 2/3
    • Probability of rolling a 6 = 1/6
    • Combined Probability = (2/3) * (1/6) = 2/18 = 1/9

  4. The spinner lands on red, and the number cube lands on 6.

    • Probability of spinner landing on red = 1/3
    • Probability of rolling a 6 = 1/6
    • Combined Probability = (1/3) * (1/6) = 1/18

Now we compare the combined probabilities from each event:

  • Event 1: 1/6
  • Event 2: 1/9
  • Event 3: 1/9
  • Event 4: 1/18

The highest likelihood is for:

The spinner lands on red, and the number cube lands on an even number (1/6).

So, this is the event with the highest likelihood of occurring.