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A company is conducting a draw to identify winners for their annual customer rewards sweepstake. It classifies its customers in 2 groups, Group A, who

A company is conducting a draw to identify winners for their annual customer rewards

sweepstake. It classifies its customers in 2 groups, Group A, who spend between $1000 and

$10,000 per year at company's stores and Group B, who spend more than $10000 per year at

company's stores. Total rewards available are 850, 200 of which are allocated only for Group

B customers; remaining 650 are available to both Group A and B. In the past years, draw was

conducted in 2 rounds, in Round 1, 200 customers from group B were selected; and in Round

2, 650 customers were selected from Group A customers and unselected Group B customers

from Round 1. But a data analyst in the company identified that this process puts Group B

customers (higher spenders) at a disadvantage. If we reverse the process, i.e. if we first select

650 customers from entire Group A and B customers and then select 200 customers from

unselected Group B customers, probability that a group B customer will win the draw will

increase by 15%.

Based on this information, if there are a total of 2000 customers in Group A and B combined,

how many customers are in Group A and Group B independently?

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