show the complete solution

II. Solve the following problems and show your complete solutions. 1. 10. A pair of dice is tossed. Find the Probability of getting: a. two odd numbers b. a sum of 5 a sum of9 c. d. a sum of7 or sum of8 e. a sum of at least 9 f. a sum of at most 5 g. asum of4 andasum 0% Find the probability distribution for the number of heads that will occur when 5 coins are tossed. Find the probability distribution for the number of tails that will occur when 4 coins are tossed. Find the probability distribution of the sum of casting a pair of dice. Find the probability distribution of the number of boys in a family with 4 children. Construct a probability distribution and histogram of the probability distribution of the number of heads when a coin is tossed 5 times. For problems 3 and 4, construct the histogram of their respective probability distributions. If X is binomially distributed with 5 trials and the probability of success is equal to 10% in each attempt, what is the probability of: a. getting exactly 4 successes? b. getting at most 3 successes? c. getting at least 1 success? Given a binomial random variable with n = 10 and p = 0.25, nd the following probabilities. a. P(X= 0) b. P(X= 3) c. P(X= 6) d. P(X s 3) e. P(X? 3) '3] random variable with n = 6 and q = 0.60. Find the a P(X = 0) b. P(X:= 1) c P(X= 2) d. P(X s 3) e. P(X 2 4) 11. What is the probability of getting exactly four 2s in casting a die 7 times? 12. Ten coins are tossed simultaneously. What is the probability that at least 3 of the results will be heads? 13. In a family with three children, find the probability of having: a. exactly 3 girls b. at most 2 boys c. at least 1 girl 14. Based on the records of the College of Business Administration, only 25% of their BS Accountancy students who are admitted to first year reaches fifth year. Assuming that this is correct, find the probability that from 20 randomly selected first year BS Accountancy students, a. exactly 15 will reach fifth year b. at most 9 will reach fifth year c. at least 17 will reach fifth year d. between 5 to 8 inclusive will reach fifth year 15. Mathematics Professor Mr. Y developed a 10-item multiple choice questions with five options in each item. If a certain student answers the questions by purely guessing, find the probability that a student will get: a. exactly 4 correct answers b. at most 3 correct answers c. at least 7 correct answers 16. Based on records, 5% of the products produced in a factory are defective. If 8 products are chosen at random from a production lot, find the probability that: a. none of them is defective b. 3 of them are defective c. at most 4 of them are defective 17. A marketing researcher found out that the leading brand of a dishwashing detergent has a 40% market share. A sample of 20 dishwashing detergent consumers was taken randomly. What is the probability that: a. five or fewer consumers will choose the leading brand? b. at least 3 consumers will choose the leading brand? c. exactly 15 consumers will choose the leading brand? 18. One of the findings of a group of marketing research students is that 47% of working mothers hold full-time jobs. If a random sample of 40 working mothers is drawn, what is the probability that: a. exactly 10 mothers will hold full-time jobs? b. at most 5 mothers will hold full-time jobs? c. at least 36 mothers will hold full-time jobs?19. Four-fifths of a certain breed of rabbits are born with thin furs. What is the probability that in a litter of five rabbits: a. exactly 4 will have thin furs? b. at most 3 will have thin furs? c. at least 2 will have thin furs? 20. If boys and girls are equally likely to be born, what is the probability that in a randomly selected family of five children, there will be: a. at least 1 girl? b. at most 2 are boys? c. exactly 3 girls? d. exactly 4 boys? e. all are boys? 21. Given that X is a Poisson random variable with / = 3. Find the following probabilities using the Poisson probability distribution formula. a. P(X = 1) b. P(X = 2) c. P(X