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Quiz 1 - Solutions

# Quiz 1 - Solutions - (a What is the probability that the...

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STATISTICS 321 – Spring 2009 – Quiz 1 (20 points) Name: SOLUTIONS 1. Suppose that vehicles taking a particular freeway exit can either turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. As an example, (a) is solved for you. (a) List all outcomes in the event A that all three vehicles go in the same direction. A = { RRR, LLL, SSS } (b) List all outcomes in the event B that all three vehicles take different directions. B = { RLS, RSL, LRS, LSR, SRL, SLR } (c) List all outcomes in the event C that exactly two of the three vehicles turn right. C = { RRS, RRL, RSR, RLR, SRR, LRR } (d) List all outcomes in the event D that exactly two of the three vehicles go in the same direction. D = { RRS, RRL, RSR, RLR, SRR, LRR, LLS, LLR, LSL, LRL, SLL, RLL, SSR, SSL, SLS, SRS, LSS, RSS } (e) List outcomes in C D and C D . Since, C is a subset of D , C D = D and C D = C . 2. It is believed that 60% of all Cal Poly students read the Tribune, 80% read the Mustang Daily, and
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Unformatted text preview: (a) What is the probability that the student reads at least one of the two newspapers? Let T = event that student reads the Tribune, M = event that student reads the Mustang Daily. Then, P ( T ) = 0 . 60 , P ( M ) = 0 . 80 , and P ( T ∩ M ) = 0 . 50. P ( T ∪ M ) = 0 . 6 + 0 . 8-. 5 = 0 . 90 (b) What is the probability that the student reads neither paper? P ( T ∪ M ) C = 1-. 9 = 0 . 10 (c) What is the probability that the student reads exactly one of the two newspapers? P ( T ∩ M C ) + P ( T C ∩ M ) = (0 . 6-. 5) + (0 . 8-. 5) = 0 . 40 OR P ( T ∪ M )-P ( T ∩ M ) = 0 . 9-. 5 = 0 . 40 3. Beethoven wrote 9 symphonies and Mozart wrote 27 piano concertos. If a university radio station announcer wishes to ﬁrst play a Beethoven symphony and then a Mozart concerto, in how many ways can this be done? 9 × 27 = 243 ways...
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