Question

2. You randomly choose a letter from (A, B, C, D, E and a friend randomly chooses a letter from fa, b, c, d, e to create a pair of 2 letters with 1 upper case letter followed by 1 lower case letter. (Note: in the English alphabet, the vowels are A, E, I, O, U.) a) Write out the sample space for this experiment. (For example one outcome in the sample space is: Ac; another is Bb.) For parts b-i use the events as defined below . Let Event H be that the pair of letters has at least one vowel . Let Event I be that the pair of letters has exactly one vowel . Let Event J be that the letters in the pair are the same . Let Event K be that the first letter in the pair comes BEFORE the second one alphabetically (e.g. the outcome Bd is in event K, but Ba and Bb are not in event K) b) Find P(H) c) Find PUC) d) Find P(K) e) Find P(I nK) f) Find P(KIJ) ) Find P(HCUJ) h) Find P((IC U K)c) i Are I and K independent? Support your answer mathematically

Answer 1

St IInd sample Ja b,c,d,ej Total Samble s bace , Ab, Ac,Ad. Ae, Ba, Bb, Bc, Bd, Be , ca , сь, cc, cd, ce Ea, Eb, Ec. Ed , Ee ,Da, Db, Depd, De l A a Elements2.5 İAq, Ab, Ac,Ad,Ae,ba , Be , Ca , ce , Da ,De, Ea , Eb,Ec h- Ed, Ee 3 I. Ab, Ac, Ad, Ba, Be, ca, ce, ba,be, tb, Ee, ed j t-İ, Aa, Ae, Bb, Bc, Bd, сь, cc, cd ,Db,Dc,Dd, Ea,ee t': Ac, Ad, Ae, Ba, 8c,Bd, Be, ca , Сь, cd , ce, Ab, ba, Dh, be, be ,Ea,Eb, ec, ed j ..İA, Ac . Ad , Ae , Bc, Bd, Be , cd, ce,De 了 bPS H No of elaments in H Total elements 2.5 No. of elaments in J Total ele ments - 2.0o 2.5

p(zcuk)e- N。of elements To tal elements 6 2.5 γ independence of and K l 2. 25 25 lo 2.5 2. 2. 5 and K are not indpendit