Page Two Question # 3-Permutation. (20 Points) (a) How many permutations are the
ID: 2929078 • Letter: P
Question
Page Two Question # 3-Permutation. (20 Points) (a) How many permutations are there of the letters in the word MISSISSIPPI? (b) How many permutations are there of the letters in the word CATARAMAN? Question # 4 Probability Rules" (10 Points) In a certain community the Probability that a man over 50 years is overweight is 0.49. The probability that his blood pressure is high given that he is overweight is 0.64. If a man over 50 years is selected at random, what is the probability that he is overweight and that he has High blood pressure ? Give your answer in the fractional format. Question # 5-Expected Value-(10 Points) A bond trader is considering the purchase of a Bond issued by a financially troubled company The price of the bond is $ 138.00. If the company avoids bankruptcy the bond will be worth $ 298.00 f the company goes bankrupt, the bond will be worth nothing. He thinks that the probability of the Company avoiding bankruptcy is 3/10. Calculate the E(x) value and give your recommendation accordingly. Question # 6, Bernoulli's Trials" ( 10 Points ) Sixty Six percent( 66%) of graduates from a certain university who apply to a law school are admitted f Fifteen (15) graduates from this university applied to Law School, What is the probability that only ine (9) of them will be accepted. e your answer in the percent formatExplanation / Answer
3. a According partition rule, that is if one is partitioning the elements of a set of N elements into k groups consisting of n1, n2, ..., nk elements (n1+n2+...+nk)=N; the number of different results is N!/n1!n2!...nk!. Thus, number of permutations for the word, which comprises 4S, 4I and 2P is:
11!/4!*2!*4!=34650
b. Applying the partition rule again, the number of possible permutations for the word CATARAMAN, which consists of 4As, 1C, 1T, 1R, 1M, and 1N respectively is as follows:
10!/4!=151200
4. Given P(overweight)=0.49, P(high blood pressure|overweight)=0.64, find P(overweight and high blood pressure).
P(high blood pressure and overweight)=P(high blood pressure|overweight)*P(overweight)=0.64*0.49=0.3136 [applying conditional probability formula, P(B|A)=P(A and B)/P(A)]
5. Assume, X denote the r.v worth of a bond. Expected value, E[X]=summation xi*pi=3/10*298+7/10*0=89.4. The price of bond, $138 is higher than expected worth, $89.4. On eshould avoid purchasing the bond.
6. From information given, p=0.66, n=15 random, independent trials, specific number of success, r=9. The probability of success is constant throughout the trials. Use Binomial distribution for Bernoulli trials. Use, P(X,r)=nCr(p)^r(1-p)^n-r.
P(X=9)=15C9(0.66)^9(1-0.66)^6=0.1837
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.