Question

please show the work on all parts

BE SURE TO SHOW YOUR WORK OR YOU WILL NOT GET CREDIT!!! 1) Jack the Ripper flips a quarter 8 times in a row. a) P(at least 1 tail) b) P(exactly 2 tails at most 3 tails) 2) You pay $2 to play a game called Saucy Jacky where you draw 2 cards from a PINOCHLE deck of cards. If you get 2 hearts, you win $10. If you get 1 heart, you get 55. Otherwise you get nothing. a) What is the expectation for this game? b) Would you play this game? Why or why not? c) What does it mean to be a fair game? d) What should the cost to play be so that this game would be a fair game?

Answer 1

e n This question follows binomial diatwibution. (x = x) = het tepi te flapy has ne number of tirats xt number of favourable P3 pacbability of favouable outcome as | Hexe pthread)' = petails '= Yence: Platteast lhead) = |- PL no heada). Á • 1 - P(X = 0) whese X =numberof heada. HP(X=0) = Cocktl80 248 Bf atdeast one head) che '60 = 2941 = 255 28 256 __b Pfexactly 2 fails at most. 3 teula). Het Xz number of tails =) p = - * *=2|*.531 = PLAXE210X533) PLX33) PCX = 2) PX23) scanned with CamScanner

اااا no p = ₂ سردار شدن عري ع تدي ع - راعي فرعععععع درمععع ع (3كغ . . = و=ع اے مر8 =n | ملا 7 عروشاريع رو= P+ ردعمه للععع هم رفتيم دوكلاع و چه را دارد گرم طلع معه + 5 + 3 + 28 + ل ی 256. 35 : مك28 ا (ععععععلها ويد ۹3 م 28 ا » Scarne with CamScanneț: الامارات

2) I PINOCHLE Cards: bit. A LAKO I 109 2 of each in all 4 suits = | There are 12 cards in each suit and a total of 48 cards. - Pl getting a beast) = 12 - -> | Pagetting a heart) - 1 - pe gesting a heast) = 1-4 - ha 57 * * P{ getting a hearts) = 1/4 1/47 - 11/188 P (not getting a heart after not getting a heart in the first try) P ( not getting a heast twice) – 3/4 x 3547 = 105 188 getting a healt once and = l-Pfnot getting a heart I not getting a heart once) S tušice) e getting a heart = 1-1/188-1051188 31-13-67788 B = 188-176 188 = 42 188 let us define X e number of hearts in a diaw of Leasde. omnScanner

| |ՍՈIԵ laj healts Let us define random vanable x = Net gain to playing the game. Ay = the number of home from the 2 cald draw. A PLY) = P(X) PTY )= P(X=-2) Then for Y = 0 ; x = -2 =) Roverete = 109/188 Yal, x PCY+1) = P(x-3) = 72/188 Y=2 i .- PC423)=P(X )=116188. (x = Amount won for number of hearts -2). . X . P(x) X. P(X). -2. 105/188 -20151188 53 721188 2161188 to 8 1/188 88/188. Expx) = 94 1188 Expectation' = E(X)= EXPG) = b). I would play the game because my net expected I gain is greater than oleh hence it is in my interest to play The game is fais when E(X)= 0 . _ ed If the cost of the game was $2.5 (half a bolle more than the current games, the expectation would be zero, hence the game would be face Scanned with damScanner1