Suppose that there are 5 blood types in the population, named type 1 through type 5, with probabilities p1, p2,. . . , p5. A crime was committed by two individuals. A suspect, who has blood type 1, has prior probability p of being guilty. At the crime scene blood evidence is collected, which shows that one of the criminals has type 1 and the other has type 2. Find the posterior probability that the suspect is guilty, given the evidence. Does the evidence make it more likely or less likely that the suspect is guilty, or does this depend on the values of the parameters p, p1,. . . , p5? If it depends, give a simple criterion for when the evidence makes it more likely that the suspect is guilty.

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be able to prepare using the sauce?

Describe how the presence of possible outliers might be identified on the following. (a) histograms gap between the first bar and the rest of bars or between the last bar and the rest of bars large group of bars to the left or right of a gap higher center bar than surrounding bars gap around the center of the histogram higher far left or right bar than surrounding bars (b) dotplots large gap around the center of the data large gap between data on the far left side or the far right side and the rest of the data large groups of data to the left or right of a gap large group of data in the center of the dotplot large group of data on the left or right of the dotplot (c) stem-and-leaf displays several empty stems in the center of the stem-and-leaf display large group of data in stems on one of the far sides of the stem-and-leaf display large group of data near a gap several empty stems after stem including the lowest values or before stem including the highest values large group of data in the center stems (d) box-and-whisker plots data within the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data within the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data beyond the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 1(iqr) and at q3 + 1(iqr)

Which equation represents h in the triangle? a) h = 6sin37° b) h = 10sin37° c) h = 6 10 sin37° d) h = 10 6 sin37°