MATH SOLVE

3 months ago

Q:
# Suppose 21% of the population are 64 or over, 27% of those 64 or over have loans, and 52% of those under 64 have loans. Find the probabilities that a person fits into the following categories. (a) 64 or over and has a loan (b) Has a loan (c) Are the events that a person is 64 or over and that the person has a loan independent? Explain.

Accepted Solution

A:

Answer:a) 0.0567b) 0.4717c) 0.099057Step-by-step explanation:Given:P( population are 64 or over ) = 21% = 0.21P( Population are under 64 ) = 1 - P( population are 64 or over )= 1 - 0.21 = 0.79P( 64 or over have loans ) = 27% = 0.27P( under 64 have loans ) = 52% = 0.52Now,a) P( 64 or over and has a loan ) = P( 64 or over have loans ) × P( population are 64 or over ) = 0.27 × 0.21= 0.0567b) P( Has a loan ) = P( population are 64 or over ) × P( 64 or over have loans ) + P( Population are under 64 ) × P( under 64 have loans ) = ( 0.21 × 0.27 ) + ( 0.79 × 0.52 )= 0.0609 + 0.4108= 0.4717c) P( events that person is 64 or over and that the person has a loan independent )= P( population are 64 or over ) × P( Has a loan ) = 0.21 × 0.4717= 0.099057