3-(35 points) Two standard 6-sided dice with 6 faces having values (1,2,3,4,5,6) are thrown and the...

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3-(35 points) Two standard 6-sided dice with 6 faces having values (1,2,3,4,5,6) are thrown and the face values on the top fa

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Answer 1

Answer #1

Following is the possible outcomes and product the outcomes of rolls of two dice:

$(1, 1) 1 (1,2) 2 (2, 1) 2 (2,2) 4 (3, 1) 3 (3, 2) 6 (1,5) 5 (2,5) 10 (3, 3) 9 (3, 4) 12 (3,5) (1,3) 3 (2,3) 6 (1,4)4 (1,6) 6$

Following is the possible outcomes and maximum the outcomes of rolls of two dice:

$(1,1) 1 (1,2) 2 (1,3) 3 (1,4) 4 (1,5) 5 (1,6)=6 (2, 1) 2 (2,2) 2 (2,3) 3 (2,4) 4 (2,5) 5 (2,6) (3, 1) 3 (3,2) 3 (3,3) 3 (3,4)$

Out of 36 outcomes, 15 outcomes show odd maximum value so

P(E) = 15 /36 = 5 /12

Out of 36 outcomes, 25 outcomes do not have 1 on any die so

P(F) = 25 / 36

Out of 36 outcomes, 14 outcomes have product less than equal to 6 so

P(G) = 14 / 36 = 7 /18

(b)

Out of 36 outcomes, 10 outcomes shows odd maximum and no 1 on any die so

$ΤΟ Ρ(EF)-Ρ(Eη F) : 36$

By the addition rule,

$15 25 10 30 P(EU F) P(E) P(F) P(En F) 36 36 36 36 1$

----------------------

Out of 36 outcomes, 5 outcomes shows maximum odd and 1 at least on a die so

$P(EF) P(En Fe) 36$

--------------------------------

Out of 36 outcomes, 3 outcomes have product less than equal to 6 and not 1 on any die so

P(FG) = 3 / 36 = 1 /12

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