1. Two draws will be made at random from a box containing 5 marbles, red, yellow, green, black and blue. The unconditional probability of getting a red marble on the first draw is 1/ 5 . The unconditional probability of getting a red marble on the second draw is 1/5 . 1. The chance that the first draw turns out to be the red marble and the second draw turns to be the red is 1 51 5 1 25when the draws are made __________ replacement, because then the events are________________. 2. The chance that the first draw turns out to be the red marble and the second draw turns to be the red is 0 when the draws are made __________ replacement, because then the events are________________. 3. The chance that at least one of the two draws turns out to be the red marble must be calculated as 1 (3 4 3 4) 5 16 when the draws are made ______________, because then the events are not ______________. 4. The chance that neither of the two draws turns out to be the red marble is 4 / 5 3 / 4 3 / 5 when the draws are made_____________________ Replacement, because then the draws are not___________________. 5. The chance that neither of the two draws turns out to be the red marble is 4 / 5 4 5 16 25 when the draws are made_____________________ Replacement, because then the draws are ___________________. Fill in the blanks using one options from each pair below for each sentence. (with, without) (independent, mutually exclusive) 2. A die is tossed 10 times, a. What is the chance of not getting a 6 spots? b. What is the chance of getting one of the 6 spots? c. What is the chance of getting five of the 6 spots? d. What is the chance of getting at least one of the 6 spots? 3. 4. 0 A machine has been designed to toss a coin automatically and keep track of the number of heads. After 1000 tosses, it has 545 heads. Express the chance error both in absolute terms and as a percentage of the number of tosses. A computer is programmed to take the sum of 400 draws made at random with replacement from the magic box: 2 4 6 8 1. 2. What is the expected value and standard error of the sum of 400 draws? 3. 5. What is the value range for the sum of 400 draws (the possible lowest value and the largest value of the sum of 400 draws)? What is the chance that the sum is less than 1500? (using the normal approximation) A coin will be tossed 400 times. (20 points) 1. Find the expected value and standard error for the number of head. 2. Estimate the chance of getting more than 220 heads