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4.13 Do Americans prefer name-brand milk or store brand milk? A survey was conducted by Harris Poll Interactive, Inc. in November 2014. Suppose the results, based on 1,138 females and 1,138 males. were as follows: GENDER PREFERENCE Male Female Total Name-Brand Milk 319 341 660 Store Brand Milk 717 649 1,366 Something Else 102 148 250 Total 1,138 1,138 2,276 Source: Data extracted from Harris Interactive, "Do Americans Prefer Name-Brands or Store Brands? Well, That Depends, bit.ly/1FpaOKI. If an American is selected at random, what is the probability that he or she a. prefers name-brand milk? b. is male and prefers name-brand milk? c. is male or prefers name-brand milk? d. Explain the difference in the results in (b) and (c).

Answer 1

According to this Question we give representation to the Preference of milk and gender and a table generate cohich shows joint probability distribution by using given table Let x- Represent the preference of milk. - Y- Represent the Gender. X1 X2 X3 represent Name - bread milk, stole Mille cand something else respectively. 41,:42 represent Gender Male and female respechvely w Prefer mille and Gender Probability : - Total Population for example, Probability that Name - bread milk and Male - PCX2441) = 3276 Probability that name- bread mille and female 341 PCX2 442) 22 76 Probability that stole Milk and Male PC*=*2 4 474) = 9276 Ret x and y be ev on Sample Space (S) X(s) : { X1,82,83} and Y(S) = {41,42} X(3) XY(S) = {XI,X2,43} x {41,42}

P;; = P(X=*;, Y:4;) lie, Pri = PX-XI AY=YI) probability of Named Milk and male Pez - PCX= 424 442) - Probability of stole Milk and female Joint Probability function of x and Y. Total YI 42 XI x2 x3 0.140 0.315 0.045 0.290 0.600 0.285 0.600 0.50 0.285 0.005 05 0.045 0.065 0.110 Total of al probability those prepes Name - breed Mille PC x x xi) PCX=X1)= [ P(X=X,4) P(x - 3): 0.40 +0.190 - P. 9 10 b) Probability and male and prefers name - bread milk. PCX = X1 X 4 =41) Pics 3.Mb Pri = 0.140

c) Probability that is male of prefers name a bread milk. (Probability of male) U ( Probability of name - breed milk) P(X=21) + PLY=Y) - 4 0.5 +0.290 -0.790 PCX2 x 1) - PC :) - 0.70 d) Difference blw & © is that In 1 find the probability of thok male who Prefer name -bread milk. Calculate PCX=XI 1 Y=419 -0.140 on ③ we have to find Probability of male in date of Union Drink (x1, x2, x3) Probability of people (Male of female) who drink named milk P(x -x) U P(Y-1): 0.740. we created joint probability fusebion table a) Probability those prefer named bread mille PC* :*) - D. 210 b) Probability og Hole mele ethio Prefer nance brand mille : 0140 c) Pobabiby of male (81, 82,83) of (comon) como Prefer name bread miles (41, 42) 70.790.