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1. 1000 candidates take SOA exam P. Countrywide, 35% will pass (SOA grade 6, whi

ID: 3303827 • Letter: 1

Question

1. 1000 candidates take SOA exam P. Countrywide, 35% will pass (SOA grade 6, while 20% will just fail (SOA Grade 5). The others will get an SOA grade under 5. The country is made of three regions: East Coast, West Coast, and Central. The coasts each have 300 candidates taking the exam. If the mark was independent of region, how many Central candidates would get a score under 5? a. Actually, the marks may be dependent. The East Coast has a 25% pass rate, while two- thirds just fail (SOA grade 5). 50 candidates pass on the West Coast Given a student passes, what's the probability the candidate was in the Central Region? b. c. Given a student does not pass, what's the probability the candidate was on the West Coast?

Explanation / Answer

a) number of central candidate taking SOA = 1000 -2*300 = 400

probability of grade under 5 = 1 - 0.35 - 0.20 = 0.45

hence

required number = 400 * 0.45 = 180

b)

total number of candidate who pass = 0.25 *300 + 50 + 400 * 0.35

= 265

required probability = 400*0.35/265 = 0.52830

c)

number of candidate who don't pass = 300 * (1-0.25) + (300 -50) + 400* (1-0.35)

= 735

required probability = 250/735

=0.340136