Consider a collection of 9 bears. There is a family of red bears consisting of one father bear, one mother bear, and one baby bear. There is a similar green bear family, and a similar blue bear family. We draw 5 consecutive times from this collection without replacement (i. e., not returning the bear after each draw). We keep track (in order) of the kind of bears that we get. 10a. Let Aj denote the event that exactly j of the red bears are chosen during the 5 draws. Do the events A0, A1, A2, A3 constitute a partition of the sample space? (As always, be sure to justify your answer.)

What is the probability of throwing several dice with sum equal to 6 (six)? show the ways of possibilities for sum 6 (as the numerator) and the ways of throwing n dices for n = 1, 2, 3, 4 or 5 as denominator for all the questions to earn full credits. (a)throw one die, (b) throw two dice, (c) throw three dice (d) throw 4 dice, (e) throw 5 dice

Calculate the total payback for a $3,500 loan at 8% annual interest with monthly payments for two years. show all of your steps. use the formula, m = pm(1 + m)^na/(1 + m)^na - 1, as needed.

Anull hypothesis states that the difference between 8 hours of sleep and 3 hours of sleep has no effect on the number of pictures a student will remember during a picture memory interface test (pmit). examining the mit database, an extremely small t-value of 0.1611 is found. this t-value is much smaller than the smallest t-value on the chart for p-value reference. from this information we can: select one: a. accept the null hypothesis because the p-value obtained shows that the difference between the two groups being tested is not statistically significant b. accept the null hypothesis because the p-value obtained was statistically significant c. reject the null hypothesis because of the p-value obtained d. reject the null hypothesis because the data obtained is statistically significant