Question

2. Drinking Warm Beer We put 10 bottles of Molson Export and 3 bottles of Labatt 50 into the trunk of our black car on a hot summer day. We reach into the the cooler, pull out a random bottle bi and drink it. Then we reach into the cooler, pull out a second bottle b2 and drink it 1. Describe the sample space S for this experiment 2. For each outcome w E S, determine Pr(w) 3. Let A be the event "b1 is a bottle of Molson Export" and let B be the event "b2 is a bottle of Labatt 50". Determine Pr(A) and Pr(B) 4. Are the events A and B independent? In other words, is Pr(A| B) Pr(A)?

Answer 1

Glven dta, Solution ro bottles of Molson Export and e Put 3 bottles of Labatt 50 iptD the trunk of ay hot Suummer our Hack car on a he veach into the cooler, Pull uta random bottle amd drink it reach into the Cooler, Pull aut a Then We oott le second amd drink it Here experiment of vhe of possible Sample Spa ce s' is an different ypes Set of all out comes of the experiment (Hol Son Export, Molson Export) (Moslon Exprrt tabatt so), (iabatt 0, MoslonEsport ),(lakatt so La batt so) S 60

2 since, out Comes, Possible Now For each outcome to determine te probahikty of W Here CMotson Export, Molson Export Then pr(w pumber of Molson Export pr(N) Total Number of bottles Aumber of remaining Molson Export X bobtles To bal numker of remaining Here Total Number of bottles =10t 3 13

pr(w) 13 90 156 since Mo tson Export = 10-i Number of Yemaining bottles 3-1 TOEal ntmer of vemaining 12 prCm) pr(w PT(w) CHolSon Export, laintt 50 pY(w) 2 13 30 156 30 PY(W 156

Pr(ws1 CLabatt 50, Holson Export) pr( X 2 13 156 Pr( 30 56 pr(w) tabatt so, Labatt s0) pr(W 3 13 /2- (56 prw4) 156

3 Let A be the vent bis a bottle of Molson Export be event bis a battle of Labatt B the y To determine Pr(A) and pr(e) Pr(A) 13 Since 30 156 prlw,)pr(w) 156 20 156 /0 13 pr CB (3 since, PYCW)PrCw) 156 56 우음

we knoo Let Consider A and B events PCANB) P(A) PlB) P (enA) P(A) P(B) PC-PA)PlA ) P(B) since conditfonal probabi ity PL P(B) Aote P(B 36 3 or (56 13 after happending P probabi lity of B event A of P P(B)

pr)Pr(A) PCAN8)= P(A) P(B) P(A). PCB) Since, conditional probakbility P) P(A) Ttisthe given assumption. t