Question

1.5.2. You have a six-sided die that you roll once. Let Ri denote the event that the roll is i. Let Gj denote the event that the roll is greater than j. Let E denote the event that the roll of the die is evennumbered. (a) What is PR3 jG1 , the conditional probability that 3 is rolled given that the roll is greater than 1

Answer 1

What is PR3 jG1 , the conditional probability that 3 is rolled given that the roll is greater than 1

=0,02

Explanation:

Sample Space for rolling a die, S(1,2,3,4,5,6]

Since all the outcomes are equally P( rolling any numebre)=1/6

G1=(2,3,4,5,6)

Hence P(G1) =P (R2)+P (R3)+P (R4)+P (R5)+P (R6)

Hence P(G1) =5/6

and R3= [3]

Hence G1 ∩ R3 = [3] = R3

Hence P(G1 ∩ R3) =P( R3) =1/6

What is PR3 jG1 , the conditional probability that 3 is rolled given that the roll is greater than 1

P(G1 ∩ R3) / P(G1) = (1/6)/ (5/6=

=0,02