3. Two fair dice are thrown. Let X be the smaller of the two numbers obtained...

Question

Question

Answer 1

Answer #1

probability mass function of X is as follows:

P(X=1)=P(at least one dice shows 1)=1-P(none of both shows 1)=1-(5/6)*(5/6)=11/36

P(X=2)=P(both dice are at least 2 and at least dice shows a 2) =9/36

P(X=3)=7/36

P(X=4)=5/36

P(X=5)=3/36

P(X=6)=1/36

hence

P(X>3)=P(X=4)+P(X=5)+P(X=6)=(5/36)+(3/36)+(1/36)=9/36=1/4

Answer 2

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