if anyone would be able to help me out with this probability question, that'd be amazing!
A die is weighted as follows:
Pr(2) = Pr(3) = Pr(4) = Pr(5) = 0.2, Pr(1) = Pr(6) = 0.1
The die is rolled twice, and the smaller of the numbers showing is noted. let Y represent this value,
Find Pr(Y = 1)
thank you in advance!
First, let's write all the possible outcomes that make up the event \(Y=1\). They are: \[(1,1),\ (1,2),\ (2,1),\ (1,3),\ (3,1),\ (1,4),\ (4,1),\ (1,5),\ (5,1),\ (1,6),\ (6,1).\] We can write down the probability of each outcome and add them up to obtain the required result. Note that some of the outcomes have the same probability \((\)eg: \(\Pr(1,2)=\Pr(2,1)\)\(\,)\)
\[\Pr(Y=1)=(0.1\times 0.1)+2(0.1\times 0.2)+2(0.1\times 0.2)+2(0.1\times 0.2)+2(0.1\times 0.2)+2(0.1\times 0.1)=\boxed{0.19\,}\]