Question

1. Assume that you have applied for two scholarships, a Leadership scholarship (denoted by L) and a Merit scholarship (denoted by M). The probability that you receive a Leadership scholarship is 0.25. The probability of receiving both scholarships is 0.15. The probability of receiving at least one of the scholarships is 0.45.

Write the probability statement using the events defined in the problem, e.g., P(L), P(M). Then compute the probability. Use 4-decimal accuracy when necessary. Please show steps.

a) [3 points] The probability that you will receive a Merit scholarship is: P(__________) = __________. Show detailed steps below.

b) [3 points] Events L and M __________ (Choose one: are, are not) mutually exclusive. Why or why not? Explain below.

c) [3 points] Events L and M __________ (Choose one: are, are not) independent. Why or why not? Explain below.

d) [3 points] The probability of receiving the Leadership scholarship given that you have been awarded the Merit scholarship is P(__________) = __________. Show detailed steps below.

e) [3 points] The probability of receiving the Merit scholarship given that you have been awarded the Leadership scholarship is: P(__________) = __________. Show detailed steps below.

Answer 1

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pabubil the schslaships that Srecuiving atteast one - ply t plH) pCLnr) 4 Nouo pat Conuidu, . we PCt PCH) PCLAH) Os-0.2T+0 18 7 freectring PCH) ment Scholar hip O Q2 . O-IS lunM) Notes 0 (Hun)d Exclu ssive Eventi July '18 16 23 Mon 30 2 Eventi Land H mot mutuall are 24 Tue 31 3 10 17 25 4 11 18 Wed 26 Thu 5 12 19 Fri 20 27 6 13 Sat 7 14 21 28 Sun 1 8 15 22 29

-for two mtually dince A amd B, ex clusie event Nouw comsider Ple PCH 2S rtaoo 22 we PC PCn) PCLAN) and H Events ndepandent mot ORe A and independent event two PANR) PLA) PCE) Now conside Leadirshep Probabilitof Scholarshipgiven thot you have bean awarded the merit Scholas ship the hecuining Notes: August '18 6 13 20 27 Mon 14 21 28 7 Tue By Cemditional Pababaly P() 8 15 22 29 Wed 1 23 30 Thu 2 9 16 PCLnH) 10 17 24 31 Fri 11 18 25 Sat .. 12 19 26 Sun 5 ... in bohavior

Thursday Pat & (L in we PCLn) PCH) FCHM) O.15 4286 PC4M)-0428 Now.cemaidery Seivngte Mexit 9iven that you have been leaderdhit&halassh Gnditional probabiy PCnL) awasded the PCC) put Eq 0 we get PCM1L) OGO00 S2.0 CMlL)0.60 Notes: July '18 Mon 30 2 16 23 . . . . Tue 31 3 10 17 24