Question

Find the probability of throwing two sixes in one toss of a pair of dice.

Short answer

The probability of throwing two sixes in one toss of a pair of dice is \(\frac{1}{36}\) or approximately 2.78%.

Step-by-step solution

Determine the sample space (possible outcomes)

When tossing a pair of dice, there are 6 possible outcomes for the first die and 6 possible outcomes for the second die. So, there are 6 × 6 = 36 possible outcomes in total.

Identify the event of interest (two sixes)

The event we are interested in, i.e. throwing two sixes, occurs only once when both dice show six. Therefore, there is 1 favorable outcome for our event of interest.

Calculate the probability

The probability of an event happening is the ratio of the number of favorable outcomes for the event to the total number of possible outcomes. In this case, the probability of throwing two sixes in one toss of a pair of dice can be calculated as: \[ P(\text{two sixes}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} = \frac{1}{36} \]

Express the probability as a fraction or a percentage

The probability of throwing two sixes in one toss of a pair of dice is \(\frac{1}{36}\). To convert this fraction to a percentage, simply multiply the fraction by 100: \[ \frac{1}{36} \times 100 \% \approx 2.78 \% \] So, the probability of throwing two sixes in one toss of a pair of dice is approximately 2.78%.