45-733 Probability and Statistics I (3rd Mini AY 1999-2000 Flex-Mode and Flex-Time)
Assignment#2 Answers
æ3öæ5ö ç ÷ç ÷ è2øè2ø P(E) = --------- æ8ö ç ÷ è4ø2.37 Clearly, there are [52 choose 2] outcomes. There are 4 Aces and there are 12 Face cards (i.e., Jacks, Queens, Kings). Hence,
æ4öæ12ö ç ÷ç ÷ è1øè 1ø P(E) = --------- æ52ö ç ÷ è 2ø2.38 The number of ways to divide the 9 motors between the three production lines is . There are 2 motors from a particular supplier and 7 not from that supplier. Hence, there are = ways to assign motors such that the 2 from the particular supplier go to the first line. Hence,
P(two to first line) =
2.51a. From Table P(A) = .4=
2.85 P = Positive Response, M = Male respondent, F = Female respondent. Hence:P(M | P^{c}) =
= = .4
2.90 F = Failure to learn and A and B are the two methods. We are given:P(A | F) =
= * = 14/17