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Assuming each possible number on a spinner has the same probability and an unbiased die is being rolled, the answer depends on how many numbers are on the spinner, and how many times the number 4 appears on each.

To find the probability, workout the probability of spinning a 4 on the spinner and the probability of rolling a 4 on the die; then as spinning the spinner has no effect on rolling the die, they are independent events and to get the probability of both happening multiply them together.

The probability of success is the number of successful outcomes divided by the total number of outcomes, giving:

Probability(spinning a 4) = how_many_4s_are_on_the_spinner / how_many_numbers_are_on_the_spinner

Probability(rolling a 4) = how_many_4s_are_on_the_die / how_many_numbers_are_on_the_die

Probability(spinning a 4 and rolling a 4) = Probability(spinning a 4) × Probability(rolling a 4)

Examples:

  • an octagonal spinner with the numbers 1-4 on it each twice and a tetrahedral die (as used in D&D games) with the numbers 1-4 on it→ pr(spin 4 & roll 4) = 2/8 × 1/4 = 1/16
  • a decagonal spinner with the numbers 0-9 and a tetrahedral die with the numbers 0-3 on it→ pr(spin 4 & roll 4) = 1/10 × 0/4 = 0
  • a decagonal spinner with the numbers 0-9 and a standard die with the numbers 1-6 on it→ pr(spin 4 & roll 4) = 1/10 × 1/6 =1/60
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Q: What is the probability that you will spin a 4 and roll a 4?
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What is the probability of spinning less then 4 on a 5 section spinner or rolling a number less then 4 on a 6 sided number cube?

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