Probability

Consider the following situation: Draw marbles randomly three times, without replacing them after a draw. There are 20 marbles overall, 8 of which are yellow, and 12 of which are green. What does the probability tree diagram to capture this setting look like? What are the respective probabilities for the events (y, y, gr) and (gr, gr, y) if the order in which the marbles are drawn does not matter? What are the respective probabilities if the order does matter? (1) 3.2) Fill in the blanks in the table. Over the last year, enrolment numbers, by gender, at a small school are as shown in the table below. For a randomly drawn student, what is the probability that the student is, (1) a) female b) a sophomore c) a male sophomore d) a female sophomore or junior e) limiting the population to the male students, a sophomore? Freshman Sophomore Junior Senior Total Female 150 100 90 93 433 Male 129 105 78 85 397 Total 279 205 168 178 830 3.3) An unbiased coin and a fair die are tossed together. (0.5) a) What is the probability of obtaining heads and a six? b) What is the probability heads or tails and a three? c) What is the probability that the coin shows tails? d) Throwing the die twice, what is the probability of heads and the sum of the die casts being seven? 3.4) Calculate the following probabilities for two dice being cast: (0.5) a) a 3 on the first die and a 5 on the second one, b) a 3 on the first one or a 5 on the second one, c) a sum of 8, d) a sum of 7 or 8, if one of the die shows a 3. 3.5) Show a diagram to represent the following situation: (0.5) Event A contains all even integers between 1 and 10 (both included) and Event B contains all integers larger than 5. 3.6) Drawing from a 52-deck of cards, what are the odds that: (0.5) a) a card is red and a king, b) a card is black or a queen, c) neither black nor a queen, d) a specific suit, say, spades? 3.7) A bowl contains four yellow chips and five black one. Drawing twice, without replacing the chips after drawing, what are the probabilities of (0.5) a) the first chip being yellow and the second one being black, b) the first chip being black and the second one yellow, c) both chips being yellow, d) both chips being black. 3.8) A bag contains four blue chips and six pink ones. As one experiment, three chips are drawn without replacement. For X taking the values of 0, 1, 2, 3 blue chips, show the probability distribution of X. How many times, out of 75 repetitions of the experiment, how often do you expect two or more blue chips being drawn? (0.5)

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