Probability with a Single Die
Probability · Class IX
Pick a target value k; see P(roll = k), P(roll <= k), P(roll > k) on a fair six-sided die.
- P(roll = k)0.1667
- P(roll <= k)0.6667
- P(roll > k)0.3333
- Odds against rolling k5
Formulas in this lab
- P(roll = k)
- P(roll <= k)
- P(roll > k)
- Odds against rolling k
Frequently asked questions
▶How is probability defined?
For an event E, $P(E) = \frac{\text{favourable outcomes}}{\text{total outcomes}}$. For a fair six-sided die, $P(\text{roll} = 4) = \frac{1}{6}$. Every probability lies between 0 (impossible) and 1 (certain).
▶How do I use this lab?
Pick a target k from 1 to 6. The lab shows $P(\text{roll} = k)$, $P(\text{roll} \le k)$, and $P(\text{roll} > k)$ as fractions and decimals. Try k = 4 to see 1/6, 4/6, and 2/6.
▶Common mistake on this topic
Students write probabilities greater than 1 or as percentages without the percent sign. Probabilities are always in $[0, 1]$ as fractions or decimals. Also, $P(\text{roll} \le k) + P(\text{roll} > k) = 1$, not 6/6 plus something extra.
▶Where do we use probability daily?
Weather forecasts ('70 percent chance of rain'), cricket-toss decisions, and Ludo dice rolls all use probability. Card games on Diwali nights are richer when you know which combinations are likely versus rare.