A bag contains 10 red marbles. 8 white marbles, and 8 blue marbles. You draw 4 m

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A bag contains 10 red marbles. 8 white marbles, and 8 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red? The probability that all the marbles are red is What is the probability that exactly two of the marbles are red? The probability that exactly two of the marbles are red is What is the probability that none of the marbles are red? The probability of picking no red marbles is A five-card poker hand is dealt at random from a standard 52-card deck. Note the total number of possible hands is C(52.5) = 2,598,960. Find the probabilities of the following scenarios: What is the probability that the hand contains exactly one ace? Answers where a = What is the probability that the hand is a flush? (That is all the cards are of the same suit: hearts, clubs, spades or diamonds.) Answer = where P What is the probability that the hand is a straight flush? Answer = , where y = A poker hand, consisting of 2 cards, is dealt from a standard deck of 52 cards. Find the probability that the hand contains 2 cards of the same suit. Your answer is: A box contains one yellow, two red. and three green balls. Two balls are randomly chosen without replacement. Define the following events: A : { One of the balls is yellow } B : { At least one ball is red } C: { Both balls are green } D : { Both balls are of the same color } Find the following conditional probabilities: P(B|A) =- P(D|B) =- P(C|A) =- Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following events: A : { A 6 does not appear on either die } B : { The sum of the numbers is even } C: { The sum of the numbers is equal to 8 The sample space for an experiment contains five sample points. The probabilities of the sample points are: P( 1) = P(2) = 0.05 P(3) = P(4) = 0.15 P( 5) = 0.6 Find the probability of each of the following events: A : { Either 1 or 2 occurs } B : { Either 1. 5, or 3 occurs } C: { 4 does not occur } P(A) = P(B) = - P(C) = If P(A) = 0.6. P(B) = 0.5 and P(ACB) =0.15. find the following probabilities: P(AUB) = P(A) =- P(B) =- P(A B) = P(A B) = The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently. Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 16 Southwest flights and observing whether they arrive on time. Find the probability that exactly 12 flights arrive on time. Would it be unusual for Southwest to have 5 flights arrive late? A quiz cosists of 20 multiple-choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %. If x is a binomial random variable, compute P(x) for each of the following cases: P(x 3), w = 5.p = 0.7 P(x) =- P(x = 0.1 P(X) =- P(x>2),n = 5.p = 0.8

Explanation / Answer

1. 15 % all red , 7.5% two red, 80% no red 2) alpha = 4 , b) 16 C) 10 3) 0.07% 4) a) 60% b)33.33% c) 18% 5) A= 33.33 B=33.33 C=33.33 6) a) 60% b) 90% c) 70%7) a) 58 b) 37 c)15 d)85 d) 80 e) 87 8) 28 % and NO 9) 54% 10) a) 0.8 b) 0.4 C) 0.7

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