Suppose that a particular type of lottery ticket yields a prize (i.e. is a winning ticket) 25% of the time. The probability that, when buying lottery tickets, the first winning ticket is obtained on the fourth purchase is? pls explain steps

Appendix A Future value of $1, FV, Period 1 2 4 7 8 13 14 D 16 CNN AN ENTRAMAMAMARIN SRANAMANIANRAINAMAMAMANI BENDR MAMA ARATA NINAMAMAMÄNIR İHİBİNİNANSAINANSMAMAN ****** ERMENEMANIN ****** 18 BIRININTEN **** KÜCKMEKAIN ****** RAMAMAMANTE 3*3*3*3 30 40 50 ****** SMART S N Na 2005 1303344 31 1350350 IN 1.010 1.020 1.030 1.041 1.051 1.062 1.083 1.094 1.105 1.116 1.127 1.138 1.149 1.161 1.173 1.184 1.196 1.208 1.220 1.282 1.348 1.489 1.645 1.020 1.040 1.061 1.082 1.104 1.149 1.172 1.195 1,219 1.243 1.268 1.294 1.319 FV = PV(1 +/)" 1.346 1.373 1.400 1.457 1.486 1.641 1.811 2.208 2.692 1.030 1.061 1.093 1.126 1.230 1.267 1.305 1.384 1.426 1.469 1.513 1.558 1.605 1.653 1.702 1.754 1.806 2.094 3.262 4.384 1.040 1.082 1.125 1.170 1.217 1.369 1.423 1.480 1.601 1.665 1.801 1.873 1.948 2.026 2.107 2.191 3.243 4.801 1.050 1.103 1.158 1.340 1.407 1.477 1.710 1.796 1.886 1.980 2.079 2.183 2.292 2.527 2.653 3.386 4.322 7.040 11.467 Percent 1.060 1.124 1.262 1.338 1.419 1.504 1.594 1.689 1.791 1.898…

Modify the Box 10.2 example on page 291 as follows: • The payouts in the three states are (Y¹, Y², Y³) = (4,3,2) • All other assumptions remain the same. Hints: Solving the problem involves applying Eq. (10.4). To see how this applies I re-write Eq. (10.4) below. U'(Y₁)q₁ = ¿E₁[U' (Ÿ₁+1)(+1+Ỹ₁+1)] U' (Y₁)q₁ = 8E₁[U' (Ỹ₁+1)(Ÿ₁+1)] +8E₁[U' (Ỹ₁+1)(+1)] where Eq. (1) matches the system of equations shown in Box 10.2. (1) ⚫ You should be able to validate that for U(c) = ln(c) implies E₁[U'(Ỹ₁+1)(Ỹ₁+1)] = 8 ⚫ To understand the Transition Matrix, assume the current state 0₁ = 1.5. The LHS is 19(1.5)=9(1.5), which is the LHS of the first equation in the system. ⚫ Since we assume we are in ₁ the Transition matrix tells us there is .5 probability of state ₁ = 1.5 eventuating in the next period so that (.5)q(1.5) = 39(1.5), which is a RHS term in the system in Box 10.2 ⚫ Apply this set-up to all three states, which generates the system shown.

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