Question

You are conducting an experiment while utilizing a six-sided die that does not produce any sort of bias towards any of the 6 numbers. You will roll this die until you achieve the number "six." A.) What is the probability that you have to roll n times? That is, you fail to roll a "six" n-1 times, then roll a six on the nth roll. B.) Sum all of the probabilities from part A. What is the significance of this value?

Answer 1

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A let and us say of "six y tettin "Six' come up as success does not come up as failure & let us define a random variable as is six comes up in ith roll siy doesnot come up in P ( X L)PCI a die and six comes up- Pixis) + PIX: 0) = 1 => P(X=0): 1- PIXI-1) ->q:1 :56 he have g this is to soll die n time to get "six" is the probability given by (n-1) failure and nth roll comes 6 PIN=n) = q lp for n=1,2,3 - - Sum & Poobanlity from part AH is given to P( N 1) + PON-2) + P (N=3) - - - - . . +357 +(a)= +(8) 3+ ...a at qt is a sum geometric progression with common satts p=/ now pc 2 so upto Infiniter terus is given 29, first team - Common rano

significance It support the is equal to g probability that axiom 1 sum of all probability