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A production process produces components of which 2% are defective. a) What is the expected number of components made before a defective one is made? b) What is the probability that the first defective component will occur within the first 10 components off the line?Tiger Woods typically sinks 75% of his short range putts on the green. If in several rounds of gold he has 11 short range attempts... a) What is the probability exactly 7 of them go in? (leave in notation form) b) What is the probability that at least one goes in? (indirect notation form) c) What is the probability that at least two go in? (indirect notation form) d) What is the expected number of putts that he should make?A game is played in which two coins are flipped at the same time. If two head comes up you win $10, if 2 tails come up you win $3, if anything else comes up you have to pay an amount Z. What amount, Z, must be paid when I head and 1 tail come up in order to ensure that the expected profit is $0 for the operator? Ie. The game is fair. A chart is provided to help you BUT YOU DO NOT NEED TO COMPLETE THE CHART. Outcome Winnings (X) Probability p(x) X*p(x) 2 heads $10.00 1 head & 1 tail ?Z? 2 tails $3 If a 1 head and 1 tail come up then you must payIt seems that every carton of eggs at the supermarket contains at least one broken egg. If, in fact, it has been determined that 3% of eggs supplied to a supermarket are cracked, what is the probability that if you buy two dozen eggs, at least one of your eggs will be cracked?A deck of cards is shuffled and cut randomly to display one card. a) What is the probability that your first "face card" will occur on the 3d cut? b) What is the probability that your first 'face' will be among the first three cards cut? c) Olivia was surprised that it took until the 5" cut before she got a heart. Should Olivia have been surprised? Determine the expected value to support your answer.1) A game is designed in which you draw 3 marbles from a bag containing 4 red and 7 white marbles. If you draw 3 red marbLes you win $10 if you draw 2 red marbles you win $2 if you draw 1 red marble you lose $1 if you draw 0 red marbles you lose $5. a) Complete a distribution table for the amount you win/lose. include an X, p(X) and my) column. b) What is the amountthat you would expect to win/lose if you played the game 10 times? A multiple-choice test has 5 questions each of which each has 4 possible answers. If you randomly select m\" a) What is the probabilitythat you get exactly 3 of the questions right? b) What is the probability you get at least one correct