Flip a Coin and Roll a Die

One coin and one six-sided die together, with every possible outcome listed for your homework.

Flip a Coin and Roll a Die

  1. Tails and 4The coin lands tails and the die shows 4, an even number.
All 12

Next step Flip the coin many timesRoll the die on its own

How it works

Each press flips a fair coin and rolls a fair six-sided die, then shows the pair, such as Tails and 4. The sample space has 2 × 6 = 12 outcomes, all equally likely, and every one is listed under the tool.

Read the full guide

Run the experiment

One press is one trial. Every trial is fresh, so the same pair can come up twice in a row. For a class experiment, press twelve times and tally each pair.

Find a probability

Count the outcomes that fit in the list under the tool and divide by 12. Heads and an even number fits three: Heads and 2, Heads and 4, Heads and 6. So the probability is 3/12 = 1/4. The shortcut is to multiply, 1/2 × 3/6 = 1/4, which works because the coin and the die do not affect each other.

Tips
  • Twelve trials rarely show each outcome exactly once. Pool several sets of twelve and the shares drift toward 1 in 12.

Questions and answers

What is the sample space when you flip a coin and roll a die?

The 12 pairs H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5 and T6, where H is heads, T is tails and the number is the die. Each has probability 1/12.

What is the probability of heads and a 6?

1/12, about 8.3%. Heads is 1/2 and a 6 is 1/6. The coin and the die do not affect each other, so you multiply: 1/2 × 1/6 = 1/12.

What is the probability of tails and a number greater than 4?

2/12, which is 1/6. Only Tails and 5 and Tails and 6 fit. The shortcut agrees: 1/2 × 2/6 = 1/6.

Why are there 12 outcomes and not 8?

You multiply, you do not add. Each of the 2 coin sides can go with each of the 6 die faces, so there are 2 × 6 = 12 pairs. 2 + 6 counts the sides, not the pairs.

More tools

Browse Numbers, Dates and Letters

All 12 outcomes

Heads 6

  • Heads and 1 The coin lands heads and the die shows 1, an odd number.
  • Heads and 2 The coin lands heads and the die shows 2, an even number.
  • Heads and 3 The coin lands heads and the die shows 3, an odd number.
  • Heads and 4 The coin lands heads and the die shows 4, an even number.
  • Heads and 5 The coin lands heads and the die shows 5, an odd number.
  • Heads and 6 The coin lands heads and the die shows 6, an even number.

Tails 6

  • Tails and 1 The coin lands tails and the die shows 1, an odd number.
  • Tails and 2 The coin lands tails and the die shows 2, an even number.
  • Tails and 3 The coin lands tails and the die shows 3, an odd number.
  • Tails and 4 The coin lands tails and the die shows 4, an even number.
  • Tails and 5 The coin lands tails and the die shows 5, an odd number.
  • Tails and 6 The coin lands tails and the die shows 6, an even number.
How this list was compiled

Arithmetic, listed by script: a coin has 2 sides and a six-sided die has 6 faces, so one flip and one roll together have 2 x 6 = 12 outcomes, Heads and 1 to Tails and 6. The script checks that there are 12, that none repeats, and that each pair of chips (heads or tails, odd or even) leaves exactly 3. The coin and the die do not affect each other, so every outcome has the same chance, 1 in 12, and the chance of two such events together is the product of their chances: Wikipedia, Independence (probability theory), https://en.wikipedia.org/wiki/Independence_(probability_theory) , read 2026-09-30 (two events are independent "if and only if their joint probability equals the product of their probabilities"). Licence: own work