Question

consider two fair 6 - sided dice, where each die has an equal chance of rolling between a 1 and a 6. which of the following, expressed as a percentage, is nearest the probability of the sum of the two dice being a number between 7 and 10, inclusive?

o 46%
o 50%
o 53%
o 57%
o 61%

Explanation:

Step1: Find total number of outcomes

Each die has 6 possible outcomes. When rolling two dice, by the multiplication - principle, the total number of outcomes is $6\times6 = 36$.

Step2: Find number of favorable outcomes

• For sum = 7: The possible combinations are $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$, so there are 6 combinations.
• For sum = 8: The possible combinations are $(2,6),(3,5),(4,4),(5,3),(6,2)$, so there are 5 combinations.
• For sum = 9: The possible combinations are $(3,6),(4,5),(5,4),(6,3)$, so there are 4 combinations.
• For sum = 10: The possible combinations are $(4,6),(5,5),(6,4)$, so there are 3 combinations.

The total number of favorable outcomes is $6 + 5+4 + 3=18$.

Step3: Calculate the probability

The probability $P$ is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{18}{36}=0.5$.
Converting to percentage, $P = 50\%$.

Answer:

50%