can someone please help me with these questionss

Part A Identify the letter of the choice that best completes the statement or answers the question by circling your choice. [1 mark each] 1. A geometric distribution has probability of failure = 0.33. Determine the expectation. a. 0.33 b. 2 c. 0.5 d. 0.66 2. What is the expected value for a binomial distribution with p =0.2 and n =6? a. 0.12 b. 0.021 c.0.276 d. 1.2 3. What is the expected number of green marbles chosen randomly from a bag containing 10 green marbles and 14 blue marbles if 6 marbles are chosen? a. 14 b.4.29 25 d.8.4 4. Predicting the number of tails when flipping a coin 50 times is an example of which distribution type? a. uniform b. binomial c. geometric d. hypergeometric 5. Nic Claxton has the worst free throw percentage in the NBA at 55%. What is the expected wait time before he misses a free throw? a. 0.55 b. 0.45 c. 1222 d.0.818 6. Which of the following values could represent the expectation for a fair game? a. 1 b.-1 c. 0 d. none of the previous choices 7. The probability of choosing any single unique card from a deck of cards is an example of which type of distribution? a. uniform b. binomial c. geometric d. hypergeometric 8. The following table is a valid probability distribution for a random variable X. What must be the value for P(2) to complete the table? a. 0.25 b.0.15 c.0.85 d.0.35 Part B Each question is marked on a 4-point scale. Please show all your thinking for full marks. 9. Arecent lottery collected $66 227 391 selling tickets at $1.50 each. The prizes were as follows: Work Space | Prize($) | NumberofPrizes | | 24000000 | 1 | o 100 000 5 1000 500 100 30 000 25 100 000 10 500 000 a. What is the probability of winning a prize in this lottery? b. Is this a fair game? Explain your thinking. 10. A 5-sided die is thrown. The faces show the number 1 through 5. a. Sketch a probability histogram for the distribution. b. Identify this distribution. [1] c. What is the expected value of this distribution? 11. The same 5-sided die from question 10 is rolled 10 times. a. What is the probability that an odd number is rolled 5 times? b. What is the expected number of odd numbers? c. What is the probability of rolling at least 2 odd numbers? 12. At a pet shop, an aquarium contains 11 piranhas and 7 baby sharks. Stephanie randomly selects 5 fish for her new aquarium. a. Find the probability that Stephanie will get at least 2 sharks. b. Calculate the expected number of piranhas. 13. Mr. Delva will play in the staff v. student softball game. He is a 0.700 hitter, which means that his probability of getting a hit when at bat is 0.70. a. What is the probability that Mr. Delva will get his first hit on his fourth at bat? b. On which at bat would you expect him to get his first hit? . What would be the probability he strikes out three times in a row. 14. The City Animal Control Department found out that 6 of the 75 squirrels that they trapped and relocated to Wolfe Island had been tagged. It was also known a total of 250 squirrels had been tagged in Kingston that season. Estimate the size of the squirrel population in Kingston? End of Test Formulas n EG) = ) % P(x) i=1 n PG) = )p*q"* . . X n: # of trials x: # of successes p: probability of success q: E(x) =np probability of failure P(x) =qg*p q: probability of failure p: probability of success X: number E(x) = % of failures P(x) = 3] by n: total available choices a: total available successes m(':) r: number of choices x: chosen successes E(x) = n Rough Work Space