In a carnival game, the player selects a ball one at a time, without replacement, from an urn containing twotwo purplepurple
ballsballs and fourfour whitewhite ballsballs. the game proceeds until a purplepurple ball is drawn. the player pays $4.004.00 to play the game and receives $1.501.50 for each ball drawn. write down the probability distribution for the player's earnings, and find its expected value.
<span>The urn contains 2 purple balls and 4 white balls. The player pay $4 for start the game and get $1.5 for every ball drawn until one purple ball is drawn. The maximal revenue would be $7.5 when 4 white balls and 1 purple balls are drawn. If the purple ball is p and white ball is w, t</span>he possible sample space of drawings are {p, wp, wwp, wwwp, wwwwp}
<span>1. Write down the probability distribution for the player earning
The player earning </span>for each event depends on the number of balls drawn subtracted the ticket price.<span> p= 2/6 The player earnings would be: 1*$1.5 -$4= - $2.5 wp= (4*2)/(6*5) = 4/15 </span>The player earnings would be: 2*1.5- $4= - $1 wwp= (4*3*2)/(6*5*4)= 1/5 The player earnings would be: 3*$1.5 -$4= $0.5 wwwp= (4*3*2*2)/(6*5*4*3*2)= 2/15 The player earnings would be: 4*$1.5 -$4= $2 wwwwp= (4*3*2*2*1)/(6*5*4*3*2*1) = 1/15 The player earnings would be: 5*$1.5 -$4= $3.5
2. Find its expected value
The expected value would be: chance of event * earning You need to combine the 5 possible outcomes from the number 1 to get the total expected value.
Total expected value= (1/3 * - 2.5)+ (4/15*-1) + (1/5*0.5) + (2/15 *2) + ( 1/15 *3.5)= (-12.5 -4 + 1.5 + 4 + 3.5) /15= -$7.5 This game basically a rip off.
