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A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form

Let's review the vitals of this question:

  • The probability of heads on a fair coin is 1/2.
  • On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability.
  • So we have a combination of outcomes below:
Outcomes
  • Heads and 4
  • Heads and 5
  • Heads and 6
  • For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities:
  • P(Heads and 4) = 1/2 * 1/6 = 1/12
  • P(Heads and 5) = 1/2 * 1/6 = 1/12
  • P(Heads and 6) = 1/2 * 1/6 = 1/12

  • Since we want any of those events, we add all three probabilities
    1/12 + 1/12 + 1/12 = 3/12

    This fraction is not simplified. So we type this fraction into our search engine, and choose Simplify.

    We get a probability of 1/4.

    By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine:
    1/4 to decimal

    Alternative Answers:

    • For a decimal, we get 0.25
    • For a percentage, we get 25%

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    Christie Applegate

    Update: 2024-05-12