A casino offers the following game a fair 6sided die numbere

A casino offers the following game: a fair 6-sided die (numbered 1 to 6) is independently thrown by you and then by the house. You win if your throw is strictly larger than that of the house, and you lose otherwise. e noise. an

Solution

Here as the game is about throwing a fair 6 sided die, each trial is independent.

Let A - your chance of winning

B - your friend win

B\' - your friend loses

i. if you are told that your friend lost.

Then friend must have thrown less than house.

Then possibilities for friend and house score are

(1,2) (1,3)...(1,6)

(2,3)....(2,6)

(3,4)...(3,6)

(4,5)(4,6)

(5,6)

There are 21 outcomes for friend losing to house.

If you have to win you have to throw more than the house.

Possibilities for winning are in case your friend loses,

(friend score, house score, your score) would be

(1,2,3) (1,2,4)...(1,2,6)

(1,3,4)(1,3,5)(1,3,6)

(1,4,5) (1,4,6)

(1,5,6) -- 10 ways

(2,3,4) (2,3,5)(2,3,6) (2,4,6) (2,5,6) (2,4,5) -- 6 ways

(3,4,5) (3,4,6) (3,5,6) -- 3 ways

(4,5,6) - 1 way

Hence prob = 20/216 =0.09259

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ii. In case your friend won the possibilities are

House, friend

=

(1,2) (1,3)...(1,6)

(2,3)....(2,6)

(3,4)...(3,6)

(4,5)(4,6)

(5,6)

Your chance of winning would be

same as that of your friend

Hence 21/216 = 0.09722

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