Respuesta :
Answer: [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
Given : You have 3 dice. For each die: Three sides are painted yellow, two sides are painted red, and one side is painted blue.
The probability of getting yellow side on any dice =[tex]\dfrac{3}{6}=\dfrac{1}{2}[/tex]
The probability of getting red side on any dice =[tex]\dfrac{2}{6}=\dfrac{1}{3}[/tex]
The probability of getting blue side on any dice =[tex]\dfrac{1}{6}[/tex]
Now, If the three dice are rolled, then the probability that they all land with the same color facing up will be :-
[tex](\dfrac{1}{2})^3+(\dfrac{1}{3})^3+ (\dfrac{1}{6})^3\\\\=\dfrac{1}{8}+\dfrac{1}{81}+\dfrac{1}{216}=\dfrac{1}{6}[/tex]
Hence, the probability that they all land with the same color facing up =[tex]\dfrac{1}{6}[/tex]
Answer:
The probability that they all land with the same color facing up is 1/6.
Step-by-step explanation:
Total number of dice = 3
Number of yellow sides in each dice = 3
Number of Red sides in each dice = 2
Number of Blue sides in each dice = 1
Let Y= Yellow color facing up, R= Red color facing up, B= Blue color facing up
[tex]P(Y)=\frac{3}{6}=\frac{1}{2}[/tex]
[tex]P(R)=\frac{2}{6}=\frac{1}{3}[/tex]
[tex]P(B)=\frac{1}{6}[/tex]
We need to find the probability that they all land with the same color facing up.
P(All dice land with the same color facing up) = P(All dice land with Yellow color facing up) + P(All dice land with Red color facing up) + P(All dice land with Blue color facing up)
[tex]P(\text{Same color})=\frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}+\frac{1}{3}\cdot \frac{1}{3}\cdot \frac{1}{3}+\frac{1}{6}\cdot \frac{1}{6}\cdot \frac{1}{6}[/tex]
[tex]P(\text{Same color})=\frac{1}{8}+\frac{1}{27}+\frac{1}{216}[/tex]
[tex]P(\text{Same color})=\frac{27+8+1}{216}[/tex]
[tex]P(\text{Same color})=\frac{1}{6}[/tex]
Therefore the probability that they all land with the same color facing up is 1/6.
