1 A shipment of thirteen smartphones contains three with cracked screens. If sold in a random order, what is the probability that the first ten sold have undamaged screens? 2 Evaluate the following...

1 A shipment of thirteen smartphones contains three with cracked screens. If sold in a random order, what is the probability that the first ten sold have undamaged screens? 2 Evaluate the following expressions (2 points each): 4P2 4C2 3 When you toss a fair six-faced die two times many outcomes can happen: (a) Determine the number of possible outcomes in the sample space. Explain your answer. (b) Calculate the probability that you get a number greater than 5 at the first toss. (c) Calculate the probability that the sum of the two tosses is at least 7. (d) Calculate the probability that the sum of the two tosses is at least 7, given that you get a number greater than 2 in the first toss. (e) If event A is “Getting a number greater than 4 in the first toss” and event B is “The sum of two tosses is at least 8”. Are event A and event B independent? Use statistical concept and mathematical expression to justify your answer. (6 points) There are sixteen shirts in your closet, eight blue and eight green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear a blue shirt on Monday and a green shirt on Tuesday. Determine whether the scenario involves independent or dependents event. Then find the probability. -Justify tour answer for full credit. If A and B are two disjoint events. If P(A) = 0.3, and P(B) = 0.4, then P(A AND B) is: (a) 0.7 (b) 0.12 (c) 0 (d) cannot be determined A random variable X follows a continuous distribution, which is symmetric to 0. If P(X =2)= 0.4, then which of the following statements are true? (There are more than one true statements). (a) P(X=-2)=0.6 (b) P(X=2)=0.4 (c) P(X=3)=0.4 (d) P(X=2)+ P(X<2)=1 (2 points) a is an event, and ac is the complement of a. which of the following statements are true? (there are more than one true statements). justify tour answer for full credit. (a) p(a and a^c )=1 (b) p(a and a^c )=0 (c) p(a or a^c )=1 (d) p(a or a^c )=0 (4 points) a group of 50 people are going to run a race. the top three runners earn gold, silver and bronze medals. determine if this scenario is a permutation or a combination, then find the number of possibilities. (4 points) you are setting the combination on a four-digit lock. you want to use the number 1234 but don´t care what order they are in. find the number of possibilities. (4 points) a small pond contains ten catfish and three bluegill. if ten fish are caught at random, what is the probability that all of them are catfish? (2="" points)="" a="" is="" an="" event,="" and="" ac="" is="" the="" complement="" of="" a.="" which="" of="" the="" following="" statements="" are="" true?="" (there="" are="" more="" than="" one="" true="" statements).="" justify="" tour="" answer="" for="" full="" credit.="" (a)="" p(a="" and="" a^c="" )="1" (b)="" p(a="" and="" a^c="" )="0" (c)="" p(a="" or="" a^c="" )="1" (d)="" p(a="" or="" a^c="" )="0" (4="" points)="" a="" group="" of="" 50="" people="" are="" going="" to="" run="" a="" race.="" the="" top="" three="" runners="" earn="" gold,="" silver="" and="" bronze="" medals.="" determine="" if="" this="" scenario="" is="" a="" permutation="" or="" a="" combination,="" then="" find="" the="" number="" of="" possibilities.="" (4="" points)="" you="" are="" setting="" the="" combination="" on="" a="" four-digit="" lock.="" you="" want="" to="" use="" the="" number="" 1234="" but="" don´t="" care="" what="" order="" they="" are="" in.="" find="" the="" number="" of="" possibilities.="" (4="" points)="" a="" small="" pond="" contains="" ten="" catfish="" and="" three="" bluegill.="" if="" ten="" fish="" are="" caught="" at="" random,="" what="" is="" the="" probability="" that="" all="" of="" them="" are="">