You play two games against the same opponent. The probability you win the first game is 0.4. If you win the first game, the probability you also win the second one is 0.2. If you lose the first game, the probability that you win the second game is 0.3.

a. Are the two games independent?
b. What's the probability you lose both games?
c. What's the probability you win both games?
d. Let random variable X be the number of games you win. Find the probability model for X complete the table below (hint: use your answers in part b and c)
X
P(x)
0
1
2
e. Find and interpret the expected value of X?
f. What is the standard deviation of X?

Fran would like to estimate the mean amount of time it takes people in her town to travel to work. the town's population is 150,000 and about 90,000 of those are working adults. which statements are true? select each correct answer. there is no way to infer the value of the mean. she must collect data for all 90,000 working adults and calculate the mean. a larger sample of working adults will provide a better estimate of the true mean than a smaller sample. the population of working adults is too large for using a sample to estimate the mean of the entire group. if she takes a random sample of the population of working adults in her town, the mean for that group is likely close to the mean for the entire group.

Adepartment store purchases screen-printed t-shirts at a cost of $5 per shirt. they mark up the price 150% (making the selling price 250% of the store's purchase price) and put them on the sales floor. every month that a t-shirt doesn't sell, the store reduces the selling price by 25%.

Abox contains 1 plain pencil and 4 pens. a second box contains 5 color pencils and 5 crayons. one item from each box is chosen at random. what is the probability that a plain pencil from the first box and a color pencil from the second box are selected? write your answer as a fraction in simplest form.