PORS UYWXYObjective: of is to learn and apply the basic rules of to themore vowels (e.g. R,T). High point tiles such as Q and Z frequently.4.2Activity 8: Using the Rules of Probabilitypopular game of Scrabble.Topics covered:1. Sample spaces2. Relative frequency and probabilityinono wsih lo ilidsdongod3. Rules of probability TTOV4. Sampling with and without replacementmomustribution of Scrabble tiles and their points are given below. As you might expect, there areOne game has 100 tiles total.Total -Letter Point Value Frequency Probability08Freg/TotalPoint' Value Frequency | Probability1 pt3 pts3 pts2 pts1 pt4 pts2 pts4 pts1 pt8 pts5 pts1 pt3 pts1 ptLetter1 pt3 pts10 pts1 ptbo.0202A.B2.2..029.4.12.12ho4.1 pt1 pt4 pts4 pts8 pts4 pts10 pts9..040202G34..022.Nlod 2 tH.2.I.0102.011.K2..044.2ZBlank.020 pts.022.9.1. Suppose we were to perform an experiment that consisted of drawing one tile from the bag.Answer the following questions for this particular experiment.(a) The sample space is all possible outcomes of a random phenomenon. Give the sample spacefor our experiment.P:{A.B.C.D.E.F.G. H. I,J, K.L,M.N.P.Q.R.S.T.U.V.W.X.Y.Z. blank(b) If the outcomes are equally likely (i.e. every tile has the same chance of being selectedankprobability of an event is defined byNumber of outcomes in the eventTotal number of outcomesP(event) =010.an 4 drau a Rdraw a blank. Becond1lit. vt events)PLA or 8)AB ore da nt (no events in common)(disioint7. Multiplication Rule (independent events)PIA and 8). PIAO8): PUA) PIR2 events A a8 areBasketbalsevent occursthe other37127711982. Now suppose our experiment consists of drawing three tiles from the bag with replacement. Thatis, after we draw each tile, we put it back in the bag before drawing the nexct tile. If any threeevents are independent, we may use the multiplication rule to calculate this probability that allthe events occur:tage in differesional sports.(a) What is the probability of drawing an A all three times? That is, we draw an A the first.time and an A the second time and an A the third time.cted game isP(A and B and C) = P(A)P(B)P(C)k) You want to draw three letters that could make a word and give you a lot of points. Comeup with such a three letter word and find the probability of picking the tiles in word orderfor our experiment (for example, if my word is CAT, then find the probability of picking aC followed by an A followed by a T). Show all the steps in your calculation.PlAn BnC) PL.09)PL.02) P(.02)won by t.3. Now suppose our experiment consists of drawing three tiles from the bag without replacement.That is, after your draw each tile, you do not put it back in the bag. This, of course, is how thegame is usually played!Probability:Word:(a) What is the probability of drawing three A's in a row for our new experiment? First findthe probability of drawing an A for your first selection using the following steps.wonHaving drawn the first A, we keep it out of the bag. This changes our chances of drawingan A the second time. Calculate this new probability of drawing an A, given that we havealready taken one out of the bag.P(first is an A) =Now two A's have been removed from the bag. Calculate the probability of drawing onemore A, given that the first and second draws were A's.P(second is an A | first is an A) =To find the probability that the first is an A and the second is an A and the third is an A,apply the general multiplication rule to the three probabilities you calculated.P(third is an A | first and second are A's) =b) Calculate the probability of drawing your high scoring three letter word from (2b) in wordorder if we select tiles without replacement.P(first is an A and second is an A and third is an A) =

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