MATH 3023 ASSIGNMENT 1-Spring 2018 1. Spin a spinner numbered 1 to 7, and toss a
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MATH 3023 ASSIGNMENT 1-Spring 2018 1. Spin a spinner numbered 1 to 7, and toss a coin. What is the probability of getting an odd number on the spinner and a tail on the coin? 2. A jar contains 6 red balls, 3 green balls, 5 white balls and 7 yellow balls. Two balls are chosen from the jar, with replacement. What is the probability that both balls chosen are green? 3. Four cards are chosen from a standard deck of $2 playing cards with replacement. What is the probability of choosing 4 hearts in a row? 4, A nationwide survey showed that 65% of all children in the United States dislike eating vegetables. If 4 children are chosen at random, what is the probability that all 4 dislike eating vegetables? (Round your answer to the nearest percent.) 5. In Europe, 88% of all households have a television. 51% of all households have a television and a VCR. What is the probability that a household has a VCR given that it has a television? 6. Suppose that, of all the customers at a coffee shop, 70% purchase a cup of coffee; 40% purchase a piece of cake; 20% purchase both a cup of coffee and a piece of cake. Given that a randomly chosen customer has purchased a piece of cake, what is the probability that he/she has also purchased a cup of coffee? 7. In a factory there are 100 units of a certain product, 5 of which are defective. We pick three units from the 100 units at random. What is the probability that exactly one of them is defective? 8. I toss a fair die twice, and obtain two numbers X and Y. Let A be the event that X-2, B be the event that X+Y-7, and C be the event that Y-3. Are A and B independent? Are A and C independent? Are B and C independent? Are A, B, and C are independent?Explanation / Answer
1:
Spinner has 7 sections numbered 1, 2, 3, 4, 5, 6, 7. Out of 7 numbers, 4 numbers are odd. So the probability of getting an odd number on spinner is
P(odd) = 4 / 7
When we tossed a coin possible outcomes are tail and head. So the probability of getting a tail is
P(tail) = 1/2
Since spinner and coin are independent because probability of getting an odd on spinner and a tail is
P(odd and tail) = P(odd)P(tail) = (4/7) * (1/2) = 2 /7 = 0.2857
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