Exam 1: Probability and Stat stics art sum is greater than Jutity your .,ws\'. t

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Exam 1: Probability and Stat stics art sum is greater than Jutity your .,ws'. that the probability of e Justify your nower inteNooly hrn two co are iped, Otherwise, coins are tossed. What is the probabiiny that two brads turs up Jusaihy yon than 3t 6. Two Saif dice are soned, what the zwotwhilty that that tho Tratnler thwVngonon will be twice the sumber appearing on the ot her Justily your an 7 In how many ways can the letters of"newjyeysouth" be arranged so that r s preceded by an s and followed by an e? Justify your EW 8. Five fair dice are relled. What is the probability that the faces showing coust iate 9. A computer has grierated seven random mrambers over the interal 0 to . mre 10. Holly puls two socks out of a drawer at random. The drawer coutains 3 red, s black mber and the other two laces show . a "full house": three of the faces show one different sumber Justify your answe likely that (a) exactly three will be in the isterval 13, 11 or (b) fres than thaee will be greater than Explain and 6 blac socks, all randomly arranged. What is the probability that the two taken are a match? Extra Credit. How many ways can the letters in the word stumgullion be arranged so that the three L's preoede all the other consonants

Explanation / Answer

Question 5:

First part of question is if the dice rolls less than 3 one coin is flipped otherwise 2. Since we need to find probability of two heads turning up, we will first find probability of dice turning up more than 3. Probability for that is 2/6 or 1/3:

Further, the probability of getting two heads 1/2 * 1/2 = 1/4

Hence the probability of tossing two heads is 1/3 * 1/4 = 1/12

Question 6:

Here we want one dice to have double the value of the other, pairings that are possible are (1,2), (2,4) and (3,6). One the first dice we might get the smaller numbers (3 possibilities) or on the second (another 3 possibilities, for a total of 6). There are 36 possible outcomes, so the probability we want is 6/36, or 1/6

Generally we answer only one question at one time. Hope this helps. Good luck

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