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: \(\Pr(1,2)=\Pr(2,1)\)\(\,)\)

\[\Pr(Y=1)=(0.1\times 0.1)+2(0.1\times 0.2)+2(0.1\times 0.2)+2(0.1\times 0.2)+2(0.1\times 0.2)+2(0.1\times 0.1)=\boxed{0.19\,}\]