Name: ___________________________________ Mark: __________/16

Deal or No Deal is an Australian game show where the contestant aims to “knock out” the lowest values of cash by randomly picking briefcases numbered 1 to 26. Each numbered briefcase contains a cash value from 50c to $200,000, which is revealed when the contestant picks that particular case. Knocking high values off the board results in less cash being won. The cash values are grouped in colours, blue being the lowest, red the middle, and green being the highest values.

     

Blue values

1. Answer  the  following  in  the  context  of  the  Deal  or  No  Deal  game  show  and  probability  theory  

a. What  is  the  main  experiment  in  the  game  show?   (1  mark)          

b. What  are  the  possible  outcomes  of  the  experiment?  (No  need  to  list  them  all,  just  a  description)   (1  mark)          

c. Describe  one  possible  event,  called  𝐴,  of  the  experiment.   (1  mark)          

d. What  is  the  complementary  event  of  𝐴?   (1  mark)          

   

Briefcase values 50c $1,000 $1 $2,000 $2 $3,000 $5 $4,000 $10 $5,000 $20 $10,000 $50 $15,000 $100 $20,000 $150 CAR $200 $50,000 $250 $75,000 $500 $100,000 $750 $200,000

Red  values  

Green  values  

2. Present  your  answers  to  the  following  questions  in  both  fraction  and  decimal  form  (to  four  significant  figures),  and  show  all  working  What  is  the  probability  that  the  first  case  opened  is:    

a. A  blue  value?   (2  marks)                

b. A  red  value?   (2  marks)                

c. A  green  value?     (2  marks)                

d. The  car?     (2  marks)              

Figure  1:  A  woman  opens  the  first  case  of  the  game,  knocking  out  the  $200,000  

3. In  July  2006,  Josh  Sharp  created  Deal  or  No  Deal  history  in  the  unluckiest  fashion  by  knocking  out  the  4  highest  cases  in  a  row,  from  $200,000  to  $50,000.  Watch  the  video  on  http://www.youtube.com/watch?v=LkaUTfUwL-­‐I&feature=plcp    

a. Let  𝐴  be  the  event  that  the  first  four  cases  opened  are  the  green  values  in  descending  order.  ($200,000,  then  $100,000,  etc.,  like  the  unlucky  man  in  the  YouTube  video.)  What  is  the  probability  of  𝐴,  𝑃(𝐴)?  Present  your  answer  as  a  fraction  and  show  all  working.     (2  marks)                  

b. Let  𝐵  be  the  event  that  the  first  four  cases  opened  are  all  green  values  (in  any  order).  What  is  the  probability  of  𝐵,  𝑃(𝐵)?  Present  your  answer  as  a  fraction  and  show  all  working.   (2  marks)  

             

Figure  2:  Josh  Sharp  opens  cases  of  the  highest  value  in  descending  order,  making  Deal  or  No  Deal  history