Question

You and a friend are playing a game. You alternate turns rolling a single die, and the first person to roll a 1 or a 2 wins. Your friend goes first.

a. What’s the probability that the game ends in three rolls or fewer?

b. What’s the expected number of rolls?

c. What’s the probability that your friend wins?

Answer 1

Ansider [you your friend your friend goes first Plowinning any person on a single trial ) = pllor 2) 릉 PO Ś three rolls or fewer (a) pl game ends in - aplegame either ends in a roll ar 2 roll or 3 roll +(35) +()(4) + ($){})(1) :*(1++4] =$($*$] a 0.7037 (6) E (number of roll ) = (number of roll ) + ( probability & nunboot ={1xş) + 2 * (**}) +3( 1)*() +44(1) ts "C's) to.

=${1+2 (1-p] +3(1-9)4+4 (1-p] +5(1-994...] Cili plis s:1+ 2(1-P)+ 3(1-P) 411421?...... (1-P) = (1-P) +2 (18+ 3(1-0)3+ --... S[1-1+P3=1+(1-P) +(1-P)?+ (1-ppt---. -Tipp = 3 E (rumbs E (number & roll ) = 1/3 1 1 1 = 3 E (numbe & roll-} (C) Pl your friend win la pl game ends in first roll) t.. a pl game ends in god roll) ton pegame ends in 5th roll) + pegame ende in 7th roll) +- +()+($$ $+()*(*)+ (3)ʻ() +--... *(1+ (5)+(3) +1+3+..] =(1-44)- - Śling) ܪܕ ]; ܢ

20.6 plyour friend win) = 0.6