A building contractor buys 70% of his cement from supplier A and 30% from supplier B. A total of 90% of the bags from A arrive undamaged , while 95% of the bags from B arrive undamaged . Give the probabilities that a damaged bag is from the following sources.

Supplier B

A manufacturing firm finds that 70% of its new hires turn out to be good workers and 30% become poor workers. All current workers are given a reasoning test. Of the good workers, 85% pass it; 35% of the poor workers pass it. Assume that these figures will hold true in the future. If the company makes the test part of its hiring procedure and only hires people who meet the previous requirements and pass the test, what percent of the new hires will turn out to be good workers?

Decide whether each exercise involves permutations or combinations, and then solve the problem.

Imagine you have a bag containing 5 red, 3 blue, and 2 orange chips.

(a) Suppose you draw a chip and it is blue. If drawing without replacement, what is the probability the next is also blue?

(b) Suppose you draw a chip and it is orange, and then you draw a second chip without replacement. What is the probability this second chip is blue?

(c) If drawing without replacement, what is the probability of drawing two blue chips in a row?

(d) When drawing without replacement, are the draws independent? Explain.

Find the solutions of the inequality by drawing appropriate graphs. State the answer correct to two decimals.

$$x^2-3 x-10 \leq 0$$

Fill in the blanks. The symbol

$$\epsilon$$

is read as "is an _____ of" and the symbol

$$\subseteq$$

is read as "is a _____ of."

Suppose you have three jars with the following contents: 2 black balls and 1 white ball in the first, 1 black ball and 2 white balls in the second, and 1 black ball and 1 white ball in the third. One jar is to be selected, and then $\mathbf{1}$ ball is to be drawn from the selected jar. If the probabilities of selecting the first, second, or third jar are $1 / 2,1 / 3$, and $1 / 6$, respectively, find the probabilities that if a white ball is drawn, it came from the following jars.
The second jar

An American tourist in Germany noticed that his taxi was travelling at 180 km/h on the autobahn. Convert this speed to miles per hour.

Which are examples of empirical probability? A weather forecast that predicts a 70 % chance of rain tomorrow.

Suppose you have three jars with the following contents: 2 black balls and 1 white ball in the first, 1 black ball and 2 white balls in the second, and 1 black ball and 1 white ball in the third. One jar is to be selected, and then 1 ball is to be drawn from the selected jar. If the probabilities of selecting the first, second, or third jar are 1/2, 1/3, and 1/6, respectively, find the probabilities that if a white ball is drawn, it came from the following jars. The third jar

List the bones of the axial skeleton and of the appendicular skeleton.

I am managing the Chicago Cubs. Suppose there is a runner on first base with nobody out and we want to determine whether we should bunt. Assume that a bunt will yield one of two results: (1) With probability .80, the bunt will be successful, in which case the batter is out and the runner on first base advances to second base. (2) With probability .20 the bunt is unsuccessful and the runner on first base is out trying to advance to second base and the batter is safe at first base. The expected number of runs that the Cubs will score in an inning in various situations is given in Table 9. TABLE 9:

$$\begin{matrix} \text{On-Base Situation} & \text{Number of Outs} & \text{Expected Number of Runs}\\\text{Runner on first} & \text{0} & \text{0.813}\\ \text{Runner on first} & \text{1} & \text{0.498}\\ \text{Runner on second} & \text{1} & \text{0.671}\\\text{Runner on second} & \text{0} & \text{1.194}\\ \text{No base runners} & \text{1} & \text{0.243}\\ \end{matrix}$$

a. If our goal is to maximize the expected number of runs scored in an inning, should we bunt? Despite this answer, why do you think teams bunt? b. If we are considering stealing second base with nobody out, what chance of success is needed for stealing second to be an optimal decision?

Suppose you have three jars with the following contents: 2 black balls and 1 white ball in the first, 1 black ball and 2 white balls in the second, and 1 black ball and 1 white ball in the third. One jar is to be selected, and then $\mathbf{1}$ ball is to be drawn from the selected jar. If the probabilities of selecting the first, second, or third jar are $1 / 2,1 / 3$, and $1 / 6$, respectively, find the probabilities that if a white ball is drawn, it came from the following jars.
The third jar

A coin is loaded so that the probability of a head occurring on a single toss is $\frac{3}{4}$. In five tosses of the coin, what is the probability of getting. All heads or all tails?