The probability of throwing two ones with a pair of dice equals _. Group of answer choices 0.3600 0.3333 0.1667 0.0278
The correct answer and explanation is:
The correct answer is 0.0278.
Explanation:
When you throw two dice, each die is independent of the other, and each die has 6 faces numbered 1 through 6.
- Total number of possible outcomes when throwing two dice:
Each die has 6 possible outcomes, so the total number of outcomes is:
6 (for the first die) × 6 (for the second die) = 36 possible outcomes. - Favorable outcome: Throwing two ones
To get two ones means the first die shows a 1 and the second die shows a 1. There is only one such outcome: (1, 1). - Calculating the probability:
The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
P(two ones)=136≈0.0278P(\text{two ones}) = \frac{1}{36} \approx 0.0278
Why the other options are incorrect:
- 0.3600 (36%): This is far too high. This would imply more than 1/3 chance, which is impossible for two specific dice faces appearing simultaneously.
- 0.3333 (33.33%): This would mean 1/3 chance, again way too high for such a specific event.
- 0.1667 (16.67%): This is 1/6, which could be the chance of getting a one on one die, but not both dice simultaneously.
Summary:
- The event “throwing two ones with a pair of dice” is a very specific, single outcome out of 36.
- The probability is therefore 136≈0.0278\frac{1}{36} \approx 0.0278.
- This means that in repeated rolls, you would expect to get double ones about 2.78% of the time.