Answer:
The probability of getting 6's on both cubes is
.
The probability that the total score is at least 11 is
.
Step-by-step explanation:
Consider the provided information.
A red cube has faces labeled 1 through 6, and a blue cube has faces labeled in the same way.
Part (A) Both cubes show 6’s.
Probability of getting 6 on red cube is ![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
Probability of getting 6 on blue cube is ![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
Thus, the probability of getting 6's on both cubes is:
![P(\text{Both 6's})=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}](https://tex.z-dn.net/?f=P%28%5Ctext%7BBoth%206%27s%7D%29%3D%5Cfrac%7B1%7D%7B6%7D%5Ctimes%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B36%7D)
Hence, the probability of getting 6's on both cubes is
.
Part (B) The total score is at least 11.
The possible number of outcomes in which total score is at least 11 is:
Red shows 6 and Blue shows 5.
Blue shows 6 and Red shows 5.
Blue shows 6 and Red shows 6.
Thus, the probability of total score is at least 11.
![P(\text{Total is at least 11})=\frac{1}{6}\times\frac{1}{6}+\frac{1}{6}\times\frac{1}{6}+\frac{1}{6}\times\frac{1}{6}\\P(\text{Total is at least 11})=\frac{1}{12}](https://tex.z-dn.net/?f=P%28%5Ctext%7BTotal%20is%20at%20least%2011%7D%29%3D%5Cfrac%7B1%7D%7B6%7D%5Ctimes%5Cfrac%7B1%7D%7B6%7D%2B%5Cfrac%7B1%7D%7B6%7D%5Ctimes%5Cfrac%7B1%7D%7B6%7D%2B%5Cfrac%7B1%7D%7B6%7D%5Ctimes%5Cfrac%7B1%7D%7B6%7D%5C%5CP%28%5Ctext%7BTotal%20is%20at%20least%2011%7D%29%3D%5Cfrac%7B1%7D%7B12%7D)
Hence, the probability that the total score is at least 11 is
.