What is the chance of throwing at least 7 in a single cast with 2 dice...
To calculate the chance of throwing at least 7 in a single cast with 2 dice, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When throwing 2 dice, each die has 6 possible outcomes (numbers 1 to 6). Since there are 2 dice, the total number of outcomes is 6 x 6 = 36.
Favorable outcomes:
To find the number of favorable outcomes, we can list all the possible combinations of numbers on the two dice that add up to at least 7:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)
- (6, 2)
- (6, 3)
- (6, 4)
- (6, 5)
There are 10 favorable outcomes in total.
Calculating the probability:
The probability of an event happening is given by the formula:
Probability = Number of favorable outcomes / Total number of outcomes.
In this case, the probability of throwing at least 7 is:
Probability = 10 / 36 = 5/18.
However, the given answer choices do not include 5/18. To choose the closest answer, we need to find the equivalent fraction for 5/18.
Equivalent fractions:
5/18 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case. So, 5/18 remains the same.
Comparing the fraction with the answer choices:
- 5/12: This is not equivalent to 5/18.
- 7/12: This is not equivalent to 5/18.
- 1/4: This is not equivalent to 5/18.
- 17/36: This is equivalent to 5/18.
Hence, the correct answer is (d) 17/36.
Note: Since the fractions 5/18 and 17/36 are equivalent, both can be considered correct answers.
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