16. Of 150 students at a school dance, 1 10 like c) Determine the probability that Alysia pop songs and 70 like heavy-metal songs. A will bowl a strike in the second, third, third of the students like both pop and and tenth frames. heavy-metal songs. ")There are ten frames in a game of a) If a pop song is played, what are the odds bowling. What is the probability that in favour of a randomly selected student Alysia will bowl a strike in the first frame liking the song? of the second game? ) What are the odds in favour of a student e) What is the long-term probability that disliking both pop and heavy-metal songs? Alysia will bowl a strike? ") Discuss any assumptions which must be ") What assumptions must be made in parts made in parts a) and b). d) and e)? 17. The four main blood types are A, B, AB, and 19. A year-long marketing study observed the O. The letters A and B indicate whether two following trends among consumers of three factors (particular molecules on the surface competing pen manufacturers. of the blood cells) are present. Thus, type . 20% of Blip Pens customers switched to AB blood has both factors while type O has Stylo and 10% switched to Glyde-Wryte. neither. Roughly 42% of the population have type A blood, 10% have type B, 3% . 15% of Stylo customers switched to have type AB, and 45% have type O. What Glyde-Wryte and 25% switched to Blip Pens. is the probability that a person a) has blood factor A? . 30% of Glyde-Wryte customers switched to Blip Pens and 5% switched to Stylo. b) does not have blood factor B? a) What is the transition matrix for this 6.6 Applying Matrices to Probability situation? Problems b) Determine the steady-state vector. ) What is the initial probability vector for this situation? b) What is the transition matrix