The probability that they are of the same colour is 19/66
The probability that at least one is red is 5/11
Explanation:Given that there are:
3 red, 4 yellow, and 5 blue marbles
Total number of marbles = 12
Two marbles are randomly selected,
1.The probability that they are of the same colour is:
(Probability that both are red) plus (the probability that both are yellow) plus (the probability that both are blue)
[tex]\begin{gathered} =(\frac{3}{12}\times\frac{2}{11})+(\frac{4}{12}\times\frac{3}{11})+(\frac{5}{12}\times\frac{4}{11}) \\ \\ =\frac{1}{22}+\frac{1}{11}+\frac{5}{33} \\ \\ =\frac{19}{66} \end{gathered}[/tex]2.The probability that at least one is red is:
1 - probability that non is red.
[tex]\begin{gathered} =1-(\frac{9}{12}\times\frac{8}{11}) \\ \\ =1-\frac{6}{11} \\ \\ =\frac{5}{11} \end{gathered}[/tex]
