In a middle school, the number of students who will take a certain elective subject depends on their grade level. This information is stored in Table A. The likelihood a student will join a particular club also depends on their grade level, with this information stored in Table B.

a. Compute the product P = AB and discuss/interpret what is indicated by the enttries P11, P13 and P24 of the product matrix.

b. How many 8th graders are expected to join the Robotics Club this year?

TABLE A.

	Number of Students	Number of Students	Number of Students
Subject	Grade 6	Grade 7	Grade 8
Music	1000	1500	500
Technology	2500	3000	2000

TABLE B.

	Likelihood of Joining a Club	Likelihood of Joining a Club	Likelihood of Joining a Club	Likelihood of Joining a Club
Grade	Chess	Robotics	Art	Dance
6	0.42	0.28	0.17	0.13
7	0.38	0.26	0.27	0.09
8	0.33	0.25	0.35	0.07